Calculus

Problem 21701

Find the tangent line to $f(t)=(e^{-t}+\sqrt{t})^{2}$ at $t=1$ . Choose from options a) to d).

See Solution

Problem 21702

Find the tangent line equation for the function $f(t)=\left(e^{-t}+\sqrt{t}\right)^{2}$ at the point $(4, f(4))$ .

See Solution

Problem 21703

Approximate the change in drug concentration $C(x)=\frac{10 x}{9+x^{2}}$ from $x=0.5$ to $x=10$ . Choices: a) 1.02 b) 5.4 c) 4.3 d) 8.5 e) 9.7

See Solution

Problem 21704

Bestimmen Sie die Intervalle für $f(x)=\frac{2}{3} x^{3}+x^{2}-12 x+1$ , den Wendepunkt von $f(x)=\frac{1}{8} x^{3}-\frac{3}{4} x^{2}-2,5$ und Extrempunkte/Schnittpunkte von $f(x)=-\frac{1}{6} x^{3}+2 x$ .

See Solution

Problem 21705

Berechnen Sie den Flächeninhalt, den der Graph von $f(x)=e^{x}+1$ , seine Tangente an der $y$ -Achse, die $x$ -Achse und die Gerade $x=-4$ begrenzen. Was ist die Tangentengleichung?

See Solution

Problem 21706

Find the monkey's acceleration at time $t=3$ for the distance $S(t)=t \sin(2t) + t^2$ . Round up the result.

See Solution

Problem 21707

Find the average rate of change of $f(x) = 2 \log_{3} x + 1$ on the interval $[1, 27]$ .

See Solution

Problem 21708

Which investment is better over 10 years: \ $11,000 at$ 6.25\% $continuously or$ 6.3\%$ semiannually?

See Solution

Problem 21709

Approximate the integral $\int_{2}^{14}(x^{2}+4)dx$ using a Riemann sum with 3 subintervals of length 4. Choose: a) 85916 b) 2758.5 c) 476 d) 608 e) None.

See Solution

Problem 21710

Approximate the change in drug concentration $C(x)=\frac{10 x}{9+x^{2}}$ for $x$ changing from 1 to 2.

See Solution

Problem 21711

Bestimmen Sie die Intervalle, in denen die Funktion $f(x)=\frac{2}{3} x^{3}+x^{2}-12 x+1$ streng monoton wächst.

See Solution

Problem 21712

Find $\lim _{x \rightarrow 0} f(x)$ for the piecewise function: $f(x)=\begin{cases} \lfloor x+3\rfloor & x<0 \\ 4 e^{-2 x} & 0 \leq x<6 \\ 2 \ln (x-2) & x \geq 6 \end{cases}$ Options: a) 2 b) 3 c) 4 d) 6 e) D.N.E

See Solution

Problem 21713

Calculate the value of a \$4,000 investment at 7% interest compounded continuously for 5 years. Options: a) \$5,400.00 b) \$5,776.27 c) \$5,610.21 d) \$5,676.27

See Solution

Problem 21714

Find the time when the drug concentration $K(x)=\frac{2 x}{x^{2}+27}$ is maximum. Options: a) $\sqrt{27}$ b) $\sqrt{16}$ c) $\sqrt{27}$ and $-\sqrt{27}$ d) $\sqrt{37}$ e) None.

See Solution

Problem 21715

Approximate the integral $\int_{1}^{13}(x^{4}+4)dx$ using 3 subintervals. Which partition is correct? a) $[1,4],[4,8],[8,13]$ b) $[1,5],[6,10],[10,14]$ c) $[1,5],[6,10],[11,13]$ d) $[1,5],[5,9],[9,13]$ e) None.

See Solution

Problem 21716

Approximate the integral $\int_{2}^{11}(x^{3}+4) dx$ using a Riemann sum with 3 subintervals of length 3. Choices: a) 1260 b) 1971 c) 5940 d) 6566 e) None.

See Solution

Problem 21717

Find the time after drug administration when the concentration $K(x)=\frac{6 x}{x^{2}+25}$ is at its maximum.

See Solution

Problem 21718

Find the monkey's acceleration at time $t=3$ for $S(t)=t \sin (2 t)+t^{3}$ . Round up your answer. Options: a) 15 b) 20 c) 26 d) 27

See Solution

Problem 21719

Find the biomass at $t=10$ hours if the average rate of change from $t=3$ to $t=10$ is $\frac{1}{7} \mathrm{mg}/$ hour and at $t=3$ it is 11.

See Solution

Problem 21720

Find the average rate of change of $y=10 \cdot 2^{\frac{x}{4}}$ from $x=4$ to $x=12$ . Round to the nearest thousandth.

See Solution

Problem 21721

Find the limit $\lim _{x \rightarrow 0} f(x)$ for the piecewise function defined as: $f(x)=\lfloor x+15\rfloor$ for $x<0$ , $14 e^{-2 x}$ for $0 \leq x<6$ , $4 \ln (x-3)$ for $x \geq 6$ .

See Solution

Problem 21722

Find the average rate of change of $y=10 \cdot 2^{\frac{x}{4}}$ from $x=4$ to $x=12$ . Round to the nearest thousandth.

See Solution

Problem 21723

Approximate the integral $\int_{1}^{13}(x^{2}+4) dx$ using a Riemann sum with 3 subintervals of length 4.

See Solution

Problem 21724

Find the integral of $12 \sin(x) \cos(x) \, dx$ . What is the result?

See Solution

Problem 21725

Approximate the integral $\int_{1}^{13}(x^{2}+4) dx$ using a Riemann sum with 3 subintervals of length 4. What are the subintervals?

See Solution

Problem 21726

Approximate the integral $\int_{1}^{10}(x^{3}+4) dx$ using a Riemann sum with 3 subintervals of length 3.

See Solution

Problem 21727

Find the critical points of $y=f(x)=4 x^{3}-6 x^{2}-72 x+3$ . Choose from the options provided.

See Solution

Problem 21728

Approximate the change in drug concentration $C(x)=\frac{10 x}{9+x^{2}}$ as $x$ changes from 0.5 to 10. Options: a) 1.02 b) 5.4 c) 4.3 d) 8.5 e) 9.7

See Solution

Problem 21729

Find the derivative of $f(x)=(x^{8}+6x)^{5}$ . Which option is correct? a) $5(x^{8}+6x)^{4}(x^{7}+1)$ b) $(x^{8}+6x)^{4}(8x^{7}+6)$ c) $5(x^{8}+6x)^{4}$ d) $5(x^{8}+6x)^{4}(8x^{7}+6)$ e) None.

See Solution

Problem 21730

Find $\frac{d y}{d t}$ for $y=\left(\tan \left(x^{8}\right)+6 x\right)^{6}$ . Choose the correct option.

See Solution

Problem 21731

Approximate the integral $\int_{1}^{13}(x^{2}+5) dx$ using a Riemann sum with 3 subintervals of length 4.

See Solution

Problem 21732

Find the time after administration when the drug concentration $K(x)=\frac{12 x}{x^{2}+25}$ is maximum: a) 25 hrs b) 5 hrs c) 5 and -5 hrs d) 30 hrs e) None.

See Solution

Problem 21733

Evaluate the integral: $\int\left(e^{4 t}+\frac{t}{3}+8\right) d t$ . Choose the correct answer from the options.

See Solution

Problem 21734

If $f$ is even and $\int_{0}^{1} f(x) dx=2$ , $\int_{0}^{3} f(x) dx=6$ , find $\int_{-1}^{3} f(x) dx$ . a) 10 b) 12 c) 8 d) 14

See Solution

Problem 21735

Find the average rate of change of $f(x) = 2 \log_{3}{x} + 1$ over the interval $[1,27]$ .

See Solution

Problem 21736

Approximate the integral $\int_{2}^{14}(x^{2}+5) dx$ using a Riemann sum with 3 subintervals of length 4.

See Solution

Problem 21737

Find the tangent line to $f(t)=(e^{-t}+\sqrt{t})^{2}$ at $(1/2, f(1/2))$ . Choose from options a) to d).

See Solution

Problem 21738

If $y=(\cos(x^{7})+5x)^{15}$ , find $\frac{dy}{dt}$ .

See Solution

Problem 21739

Find the total reaction to a drug from $t=1$ to $t=10$ for $R^{\prime}(t)=\frac{6}{t}+\frac{4}{t^{3}}+e^{-2 t}$ . Round up.

See Solution

Problem 21740

Calculate the volume of the solid formed by revolving the area bounded by $x=y^{3/2}$ , $x=0$ , $y=2$ around the y-axis.

See Solution

Problem 21741

Find the time $x$ when the drug concentration $K(x)=\frac{4 x}{x^{2}+20}$ is at its maximum.

See Solution

Problem 21742

Find the derivative of the function $f(x)=(x^{3}+6x)^{4}$ . What is $\frac{d f(x)}{d x}$ ?

See Solution

Problem 21743

Calculate the integral $\int_{1}^{10}(x^{3}+4) dx$ using a Riemann sum with 3 subintervals and midpoints.

See Solution

Problem 21744

A bacteria culture grows proportionally. At 6:00 AM, there are 4,000 bacteria; at noon, there are 4,800. Find the count at midnight.
There will be about $\square$ bacteria at midnight.

See Solution

Problem 21745

Find the integral of $4 e^{4 t}+\frac{t}{3}+4$ : a) $e^{4 t}+\frac{t^{2}}{6}+4 t+C$ b) $\frac{e^{4 t}}{4}+\frac{t^{2}}{3}+4 t+C$ c) $\frac{e^{4 t}}{4}+\frac{t^{2}}{2}+t+C$ d) $e^{4 t}+\frac{t^{2}}{2}+C$ e) None of the above

See Solution

Problem 21746

Find $\int_{-2}^{5} f(x) d x$ given that $f$ is even and $\int_{0}^{2} f(x) dx=1$ , $\int_{0}^{5} f(x) dx=4$ .

See Solution

Problem 21747

Find $\frac{d f(x)}{d x}$ for $f(x)=(x^{3}+6x^{2})^{4}$ . Choose the correct option: a) b) c) d) e).

See Solution

Problem 21748

Calcule o valor de $k$ na equação $T(t)=20+100 e^{-k t}$ , dado que $T(t_1)=30^{\circ} \mathrm{C}$ . Opções: (A) $\ln \frac{10}{t_{1}}$ , (B) $t_{1}-\ln 10$ , (C) $\frac{\ln 10}{t_{1}}$ , (D) $t_{1}+\ln 10$ .

See Solution

Problem 21749

Approximate the integral $\int_{1}^{13}(x^{2}+5) dx$ using a Riemann sum with 3 subintervals of length 4.

See Solution

Problem 21750

Find the volume of the solid formed by rotating the area between $y = \sqrt{x}$ and $y = x^{2}$ around the x-axis.

See Solution

Problem 21751

Find $\frac{d y}{d t}$ for $y=\left(\sin \left(x^{8}\right)+6\right)^{6}$ . Choices include derivatives involving $x$ .

See Solution

Problem 21752

Evaluate the integral of $(\sin(x))^8 \cos(x) \, dx$ . What is the result? a) $\frac{(\cos(x))^9}{9}+C$ b) $\frac{(\sin(x))^9}{9}+C$ c) $8(\sin(x))^2+C$ d) $8(\cos(x))^2+C$ e) None of the above

See Solution

Problem 21753

Bestimme den Grenzwert $\varlimsup_{n \to \infty} a_{n}$ für die Folge $a_{n}=5+\frac{4}{n}-\left(\frac{1}{n^{2}}+2\right)$ .

See Solution

Problem 21754

Find the total reaction from the $2^{\text{nd}}$ to the $10^{\text{th}}$ hour given $R^{\prime}(t)=\frac{6}{t}+\frac{4}{t^{3}}+e^{-2t}$ . Round up to the nearest whole number. Options: a) 7 b) 9 c) 12 d) 11

See Solution

Problem 21755

What time after administration does the drug concentration $K(x)=\frac{6x}{x^{2}+25}$ peak?

See Solution

Problem 21756

Find the tangent line to the curve $f(t)=\left(e^{-t}+\sqrt{t}\right)^{2}$ at the point $(2, f(2))$ .

See Solution

Problem 21757

Find the tangent line equation for $f(t)=\left(e^{-t}+\sqrt{t}\right)^{2}$ at $(3, f(3))$ .

See Solution

Problem 21758

Find the total reaction to a drug from the 2nd to the 8th hour given the rate $R^{\prime}(t)=\frac{4}{t}+\frac{3}{t^{3}}+e^{-2 t}$ . Round up your answer.

See Solution

Problem 21759

Find the derivative of $f(x)=(x^{3}+6x)^{4}$ . Which option is correct? a) b) c) d) e)

See Solution

Problem 21760

Approximate the integral $\int_{2}^{14}(x^{2}+3) dx$ using a Riemann sum with 3 subintervals of length 4.

See Solution

Problem 21761

Find the total reaction from hour 1 to hour 10 for $R^{\prime}(t)=\frac{4}{t}+\frac{3}{t^{3}}+e^{-2 t}$ . Round up.

See Solution

Problem 21762

Find $\frac{d y}{d t}$ for $y=\left(\tan \left(x^{5}\right)+5\right)^{6}$ . Choose the correct option.

See Solution

Problem 21763

Evaluate the integral $\int(\sin (x))^{12}(\cos (x)) d x$ and choose the correct answer from the options.

See Solution

Problem 21764

Approximate the integral $\int_{1}^{13}(x^{2}+5) dx$ using a Riemann sum with 3 subintervals of length 4. Choices: a) 488 b) 1160 c) 2879 d) 8591 e) None.

See Solution

Problem 21765

Approximate the integral $\int_{1}^{10}(x^{3}+4) dx$ using a Riemann sum with 3 subintervals of length 3. Choices: a) 1260 b) 1345 c) 2758.5 d) 4257 e) None.

See Solution

Problem 21766

Approximate the integral $\int_{2}^{14}(x^{2}+3) dx$ using a Riemann sum with 3 subintervals of length 4.

See Solution

Problem 21767

If $f$ is even and $\int_{0}^{3} f(x) dx=-2$ , $\int_{0}^{4} f(x) dx=3$ , find $\int_{-3}^{4} f(x) dx$ .

See Solution

Problem 21768

Find the derivative of the function $f(x)=(x^{3}+4x)^{3}$ . What is $\frac{d f(x)}{d x}$ ?

See Solution

Problem 21769

Find $\int_{-3}^{4} f(x) d x$ if $f$ is even, $\int_{0}^{3} f(x) d x=-2$ , and $\int_{0}^{4} f(x) d x=3$ .

See Solution

Problem 21770

Approximate the integral $\int_{2}^{11}(x^{3}+4)dx$ using 3 subintervals. Which partition is correct? a) b) c) d) e) None.

See Solution

Problem 21771

Find $\int_{-2}^{6} f(x) d x$ given that $f$ is even, $\int_{0}^{2} f(x) d x=1$ , and $\int_{0}^{6} f(x) d x=3$ .

See Solution

Problem 21772

Find the monkey's acceleration at time $t=3$ for the distance function $S(t)=t \sin (2 t)+t^{2}$ , rounding up results.

See Solution

Problem 21773

Approximate the change in drug concentration $C(x)=\frac{10 x}{9+x^{2}}$ from $x=0.5$ to $x=1.5$ .

See Solution

Problem 21774

Bestimme die Normalengleichung für $f$ an den Punkten A: a) $f(x)=x^{3}+\frac{26}{27}$ , b) $f(x)=x^{2}+5x+\frac{4}{3}$ , c) $f(x)=\frac{2}{x}+\frac{1}{4}x+\frac{3}{2}$ , d) $f(x)=\sqrt{x}-x+2$ .

See Solution

Problem 21775

Set up the integral for $\int_{C} y^{3} dx + (x^{3} + 8xy^{2}) dy$ where $C: \vec{r}(t)=<2 \cos(t), 2 \sin(t)>$ , $0 \leq t \leq 2\pi$ .

See Solution

Problem 21776

Approximate the integral $\int_{1}^{10}(x^{4}+4) dx$ using a Riemann sum with 3 subintervals of length 3.

See Solution

Problem 21777

Find the integral of $e^{3 t} + t + 5$ with respect to $t$ . Choose the correct answer from the options.

See Solution

Problem 21778

Find the total reaction from $t=1$ to $t=10$ for $R^{\prime}(t)=\frac{6}{t}+\frac{4}{t^{3}}+e^{-2 t}$ . Round up. a) 16 b) 17 c) 14 d) 21

See Solution

Problem 21779

Logistic growth function $f(t)=\frac{160}{1+9 e^{-0.165 t}}$ describes elk population. Find: A. Initial elk, B. Elk after 10 years, C. Limiting population.

See Solution

Problem 21780

Approximate the change in drug concentration $C(x)=\frac{10 x}{9+x^{2}}$ for $x$ changing from 1 to 1.5.

See Solution

Problem 21781

Zeigen Sie, dass $F(x)=(x-2) \cdot e^{x}$ eine Stammfunktion von $f(x)=(x-1) \cdot e^{x}$ ist und berechnen Sie $\int_{a}^{1} f(x) d x$ .

See Solution

Problem 21782

Calculate the integral: $\int 12 \sin (x) \cos (x) d x$

See Solution

Problem 21783

Find the difference quotient for $f(x) = \sqrt{3x + 8}$ in simplest form.

See Solution

Problem 21784

If $f$ is even and $\int_{0}^{1} f(x) dx=2$ , $\int_{0}^{6} f(x) dx=7$ , find $\int_{-1}^{6} f(x) dx$ .

See Solution

Problem 21785

Find the tangent line equation to $f(t)=(e^{-2 t}+\sqrt{t})^{2}$ at $(3, f(3))$ . Choose the correct option.

See Solution

Problem 21786

Finde die Normalen-Gleichung an den Graphen von f in den Punkten A für die Funktionen: a) $f(x)=x^{3}+\frac{26}{27}$ , b) $f(x)=x^{2}+5 x+\frac{4}{3}$ , c) $f(x)=\frac{2}{x}+\frac{1}{4} x+\frac{3}{2}$ , d) $f(x)=\sqrt{x}-x+2$ .

See Solution

Problem 21787

If $f$ is even and $\int_{0}^{1} f(x) dx=2$ , $\int_{0}^{6} f(x) dx=7$ , find $\int_{-1}^{6} f(x) dx$ .

See Solution

Problem 21788

Differentiate and optimize the equation $5 x^{2}+4 x-32$ . Find $x=$ and state if it's a max or min value (1.d.p).

See Solution

Problem 21789

Berechnen Sie den Flächeninhalt $A$ unter der Funktion $f(x) = (x - 1) \cdot e^x$ von $-\infty$ bis $1$ .

See Solution

Problem 21790

Zeigen Sie, dass es genau ein $k > 1$ gibt, sodass $\int_{-1}^{k} (x - 1) \cdot e^x \, dx = 0$ . Schätzen Sie $k$ ab.

See Solution

Problem 21791

Set up the integral $\int_{S} (x^{2}+y^{2}+z^{2}) dS$ for the surface $z=x+y$ within the cylinder $x^{2}+y^{2}=4$ .

See Solution

Problem 21792

Zeigen Sie, dass es genau ein $k>1$ mit $\int_{-1}^{k} f(x) \, dx=0$ gibt. Schätzen Sie $k$ und erklären Sie Ihre Schätzung. Berechnen Sie $\int_{1}^{2} f(x) \, dx$ und klären Sie, ob $k \geq 2$ oder $k<2$ gilt. Die Funktion ist $f(x)= (x-1) \cdot e^x$ .

See Solution

Problem 21793

Evaluate the line integral $\int_{C} x y d s$ where $C$ is the line $y=3 x$ from $(0,0)$ to $(3,9)$ .

See Solution

Problem 21794

Calculate the integral: $\int(x+1)^{2} x^{5} dx$ . Hint: Use algebraic manipulation.

See Solution

Problem 21795

Berechnen Sie den Wert von $\int_{1}^{2} (x-1) e^x \, dx$ und bestimmen Sie, ob $k \geq 2$ oder $k < 2$ gilt.

See Solution

Problem 21796

Find the partial derivative of $4xy + 6x^{\frac{3}{2}}y^{-\frac{1}{2}}$ with respect to $y$ at the point $(1,1)$ .

See Solution

Problem 21797

Find the derivative of $4xy + 6x^{\frac{3}{2}}y^{-\frac{1}{2}}$ with respect to $y$ and set it equal to 10.

See Solution

Problem 21798

Bestimme $\varlimsup_{n \in \mathbb{N}} b_{n} = \frac{n-1}{n+1}$ und analysiere die Monotonie.

See Solution

Problem 21799

Find $\lim _{x \rightarrow 0} f(x)$ for the piecewise function: $f(x)=\lfloor x+8\rfloor$ if $x<0$ , $4 e^{-2 x}$ if $0 \leq x<6$ , and $2 \ln (x-2)$ if $x \geq 6$ . Choices: a) 3 b) 2 c) 4 d) 6 e) D.N.E.

See Solution

Problem 21800

Differentiate implicitly to find $\frac{d y}{d x}$ and the slope at the point (4,1) for $3xy + 6x^{3/2}y^{-1/2} = 60$ .

See Solution

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Calculus

Problem 21701

Find the tangent line to f(t)=(e−t+t)2f(t)=(e^{-t}+\sqrt{t})^{2}f(t)=(e−t+t​)2 at t=1t=1t=1. Choose from options a) to d).

Problem 21702

Find the tangent line equation for the function f(t)=(e−t+t)2f(t)=\left(e^{-t}+\sqrt{t}\right)^{2}f(t)=(e−t+t​)2 at the point (4,f(4))(4, f(4))(4,f(4)).

Problem 21703

Approximate the change in drug concentration C(x)=10x9+x2C(x)=\frac{10 x}{9+x^{2}}C(x)=9+x210x​ from x=0.5x=0.5x=0.5 to x=10x=10x=10. Choices: a) 1.02 b) 5.4 c) 4.3 d) 8.5 e) 9.7

Problem 21704

Problem 21705

Berechnen Sie den Flächeninhalt, den der Graph von f(x)=ex+1f(x)=e^{x}+1f(x)=ex+1, seine Tangente an der yyy-Achse, die xxx-Achse und die Gerade x=−4x=-4x=−4 begrenzen. Was ist die Tangentengleichung?

Problem 21706

Find the monkey's acceleration at time t=3t=3t=3 for the distance S(t)=tsin⁡(2t)+t2S(t)=t \sin(2t) + t^2S(t)=tsin(2t)+t2. Round up the result.

Problem 21707

Find the average rate of change of f(x)=2log⁡3x+1f(x) = 2 \log_{3} x + 1f(x)=2log3​x+1 on the interval [1,27][1, 27][1,27].

Problem 21708

Which investment is better over 10 years: \11,000at11,000 at 11,000at6.25\%continuouslyor continuously or continuouslyor6.3\%$ semiannually?

Problem 21709

Approximate the integral ∫214(x2+4)dx\int_{2}^{14}(x^{2}+4)dx∫214​(x2+4)dx using a Riemann sum with 3 subintervals of length 4. Choose: a) 85916 b) 2758.5 c) 476 d) 608 e) None.

Problem 21710

Approximate the change in drug concentration C(x)=10x9+x2C(x)=\frac{10 x}{9+x^{2}}C(x)=9+x210x​ for xxx changing from 1 to 2.

Problem 21711

Bestimmen Sie die Intervalle, in denen die Funktion f(x)=23x3+x2−12x+1f(x)=\frac{2}{3} x^{3}+x^{2}-12 x+1f(x)=32​x3+x2−12x+1 streng monoton wächst.

Problem 21712

Problem 21713

Calculate the value of a \$4,000 investment at 7% interest compounded continuously for 5 years. Options: a) \$5,400.00 b) \$5,776.27 c) \$5,610.21 d) \$5,676.27

Problem 21714

Find the time when the drug concentration K(x)=2xx2+27K(x)=\frac{2 x}{x^{2}+27}K(x)=x2+272x​ is maximum. Options: a) 27\sqrt{27}27​ b) 16\sqrt{16}16​ c) 27\sqrt{27}27​ and −27-\sqrt{27}−27​ d) 37\sqrt{37}37​ e) None.

Problem 21715

Problem 21716

Approximate the integral ∫211(x3+4)dx\int_{2}^{11}(x^{3}+4) dx∫211​(x3+4)dx using a Riemann sum with 3 subintervals of length 3. Choices: a) 1260 b) 1971 c) 5940 d) 6566 e) None.

Problem 21717

Find the time after drug administration when the concentration K(x)=6xx2+25K(x)=\frac{6 x}{x^{2}+25}K(x)=x2+256x​ is at its maximum.

Problem 21718

Find the monkey's acceleration at time t=3t=3t=3 for S(t)=tsin⁡(2t)+t3S(t)=t \sin (2 t)+t^{3}S(t)=tsin(2t)+t3. Round up your answer. Options: a) 15 b) 20 c) 26 d) 27

Problem 21719

Find the biomass at t=10t=10t=10 hours if the average rate of change from t=3t=3t=3 to t=10t=10t=10 is 17mg/\frac{1}{7} \mathrm{mg}/71​mg/hour and at t=3t=3t=3 it is 11.

Problem 21720

Find the average rate of change of y=10⋅2x4y=10 \cdot 2^{\frac{x}{4}}y=10⋅24x​ from x=4x=4x=4 to x=12x=12x=12. Round to the nearest thousandth.

Problem 21721

Find the limit lim⁡x→0f(x)\lim _{x \rightarrow 0} f(x)limx→0​f(x) for the piecewise function defined as: f(x)=⌊x+15⌋f(x)=\lfloor x+15\rfloorf(x)=⌊x+15⌋ for x<0x<0x<0, 14e−2x14 e^{-2 x}14e−2x for 0≤x<60 \leq x<60≤x<6, 4ln⁡(x−3)4 \ln (x-3)4ln(x−3) for x≥6x \geq 6x≥6.

Problem 21722

Find the average rate of change of y=10⋅2x4y=10 \cdot 2^{\frac{x}{4}}y=10⋅24x​ from x=4x=4x=4 to x=12x=12x=12. Round to the nearest thousandth.

Problem 21723

Approximate the integral ∫113(x2+4)dx\int_{1}^{13}(x^{2}+4) dx∫113​(x2+4)dx using a Riemann sum with 3 subintervals of length 4.

Problem 21724

Find the integral of 12sin⁡(x)cos⁡(x) dx12 \sin(x) \cos(x) \, dx12sin(x)cos(x)dx. What is the result?

Problem 21725

Approximate the integral ∫113(x2+4)dx\int_{1}^{13}(x^{2}+4) dx∫113​(x2+4)dx using a Riemann sum with 3 subintervals of length 4. What are the subintervals?

Problem 21726

Approximate the integral ∫110(x3+4)dx\int_{1}^{10}(x^{3}+4) dx∫110​(x3+4)dx using a Riemann sum with 3 subintervals of length 3.

Problem 21727

Find the critical points of y=f(x)=4x3−6x2−72x+3y=f(x)=4 x^{3}-6 x^{2}-72 x+3y=f(x)=4x3−6x2−72x+3. Choose from the options provided.

Problem 21728

Approximate the change in drug concentration C(x)=10x9+x2C(x)=\frac{10 x}{9+x^{2}}C(x)=9+x210x​ as xxx changes from 0.5 to 10. Options: a) 1.02 b) 5.4 c) 4.3 d) 8.5 e) 9.7

Problem 21729

Problem 21730

Find dydt\frac{d y}{d t}dtdy​ for y=(tan⁡(x8)+6x)6y=\left(\tan \left(x^{8}\right)+6 x\right)^{6}y=(tan(x8)+6x)6. Choose the correct option.

Problem 21731

Approximate the integral ∫113(x2+5)dx\int_{1}^{13}(x^{2}+5) dx∫113​(x2+5)dx using a Riemann sum with 3 subintervals of length 4.

Problem 21732

Find the time after administration when the drug concentration K(x)=12xx2+25K(x)=\frac{12 x}{x^{2}+25}K(x)=x2+2512x​ is maximum: a) 25 hrs b) 5 hrs c) 5 and -5 hrs d) 30 hrs e) None.

Problem 21733

Evaluate the integral: ∫(e4t+t3+8)dt\int\left(e^{4 t}+\frac{t}{3}+8\right) d t∫(e4t+3t​+8)dt. Choose the correct answer from the options.

Problem 21734

If fff is even and ∫01f(x)dx=2\int_{0}^{1} f(x) dx=2∫01​f(x)dx=2, ∫03f(x)dx=6\int_{0}^{3} f(x) dx=6∫03​f(x)dx=6, find ∫−13f(x)dx\int_{-1}^{3} f(x) dx∫−13​f(x)dx. a) 10 b) 12 c) 8 d) 14

Problem 21735

Find the average rate of change of f(x)=2log⁡3x+1f(x) = 2 \log_{3}{x} + 1f(x)=2log3​x+1 over the interval [1,27][1,27][1,27].

Problem 21736

Approximate the integral ∫214(x2+5)dx\int_{2}^{14}(x^{2}+5) dx∫214​(x2+5)dx using a Riemann sum with 3 subintervals of length 4.

Problem 21737

Find the tangent line to f(t)=(e−t+t)2f(t)=(e^{-t}+\sqrt{t})^{2}f(t)=(e−t+t​)2 at (1/2,f(1/2))(1/2, f(1/2))(1/2,f(1/2)). Choose from options a) to d).

Problem 21738

If y=(cos⁡(x7)+5x)15y=(\cos(x^{7})+5x)^{15}y=(cos(x7)+5x)15, find dydt\frac{dy}{dt}dtdy​.

Problem 21739

Find the total reaction to a drug from t=1t=1t=1 to t=10t=10t=10 for R′(t)=6t+4t3+e−2tR^{\prime}(t)=\frac{6}{t}+\frac{4}{t^{3}}+e^{-2 t}R′(t)=t6​+t34​+e−2t. Round up.

Problem 21740

Calculate the volume of the solid formed by revolving the area bounded by x=y3/2x=y^{3/2}x=y3/2, x=0x=0x=0, y=2y=2y=2 around the y-axis.

Problem 21741

Find the time xxx when the drug concentration K(x)=4xx2+20K(x)=\frac{4 x}{x^{2}+20}K(x)=x2+204x​ is at its maximum.

Problem 21742

Find the tangent line to $f(t)=(e^{-t}+\sqrt{t})^{2}$ at $t=1$ . Choose from options a) to d).

Find the tangent line equation for the function $f(t)=\left(e^{-t}+\sqrt{t}\right)^{2}$ at the point $(4, f(4))$ .

Approximate the change in drug concentration $C(x)=\frac{10 x}{9+x^{2}}$ from $x=0.5$ to $x=10$ . Choices: a) 1.02 b) 5.4 c) 4.3 d) 8.5 e) 9.7

Berechnen Sie den Flächeninhalt, den der Graph von $f(x)=e^{x}+1$ , seine Tangente an der $y$ -Achse, die $x$ -Achse und die Gerade $x=-4$ begrenzen. Was ist die Tangentengleichung?

Find the monkey's acceleration at time $t=3$ for the distance $S(t)=t \sin(2t) + t^2$ . Round up the result.

Find the average rate of change of $f(x) = 2 \log_{3} x + 1$ on the interval $[1, 27]$ .

Which investment is better over 10 years: \ $11,000 at$ 6.25\% $continuously or$ 6.3\%$ semiannually?

Approximate the integral $\int_{2}^{14}(x^{2}+4)dx$ using a Riemann sum with 3 subintervals of length 4. Choose: a) 85916 b) 2758.5 c) 476 d) 608 e) None.

Approximate the change in drug concentration $C(x)=\frac{10 x}{9+x^{2}}$ for $x$ changing from 1 to 2.

Bestimmen Sie die Intervalle, in denen die Funktion $f(x)=\frac{2}{3} x^{3}+x^{2}-12 x+1$ streng monoton wächst.

Find the time when the drug concentration $K(x)=\frac{2 x}{x^{2}+27}$ is maximum. Options: a) $\sqrt{27}$ b) $\sqrt{16}$ c) $\sqrt{27}$ and $-\sqrt{27}$ d) $\sqrt{37}$ e) None.

Approximate the integral $\int_{2}^{11}(x^{3}+4) dx$ using a Riemann sum with 3 subintervals of length 3. Choices: a) 1260 b) 1971 c) 5940 d) 6566 e) None.

Find the time after drug administration when the concentration $K(x)=\frac{6 x}{x^{2}+25}$ is at its maximum.

Find the monkey's acceleration at time $t=3$ for $S(t)=t \sin (2 t)+t^{3}$ . Round up your answer. Options: a) 15 b) 20 c) 26 d) 27

Find the biomass at $t=10$ hours if the average rate of change from $t=3$ to $t=10$ is $\frac{1}{7} \mathrm{mg}/$ hour and at $t=3$ it is 11.

Find the average rate of change of $y=10 \cdot 2^{\frac{x}{4}}$ from $x=4$ to $x=12$ . Round to the nearest thousandth.

Find the limit $\lim _{x \rightarrow 0} f(x)$ for the piecewise function defined as: $f(x)=\lfloor x+15\rfloor$ for $x<0$ , $14 e^{-2 x}$ for $0 \leq x<6$ , $4 \ln (x-3)$ for $x \geq 6$ .

Find the average rate of change of $y=10 \cdot 2^{\frac{x}{4}}$ from $x=4$ to $x=12$ . Round to the nearest thousandth.

Approximate the integral $\int_{1}^{13}(x^{2}+4) dx$ using a Riemann sum with 3 subintervals of length 4.

Find the integral of $12 \sin(x) \cos(x) \, dx$ . What is the result?

Approximate the integral $\int_{1}^{13}(x^{2}+4) dx$ using a Riemann sum with 3 subintervals of length 4. What are the subintervals?

Approximate the integral $\int_{1}^{10}(x^{3}+4) dx$ using a Riemann sum with 3 subintervals of length 3.

Find the critical points of $y=f(x)=4 x^{3}-6 x^{2}-72 x+3$ . Choose from the options provided.

Approximate the change in drug concentration $C(x)=\frac{10 x}{9+x^{2}}$ as $x$ changes from 0.5 to 10. Options: a) 1.02 b) 5.4 c) 4.3 d) 8.5 e) 9.7

Find $\frac{d y}{d t}$ for $y=\left(\tan \left(x^{8}\right)+6 x\right)^{6}$ . Choose the correct option.

Approximate the integral $\int_{1}^{13}(x^{2}+5) dx$ using a Riemann sum with 3 subintervals of length 4.

Find the time after administration when the drug concentration $K(x)=\frac{12 x}{x^{2}+25}$ is maximum: a) 25 hrs b) 5 hrs c) 5 and -5 hrs d) 30 hrs e) None.

Evaluate the integral: $\int\left(e^{4 t}+\frac{t}{3}+8\right) d t$ . Choose the correct answer from the options.

If $f$ is even and $\int_{0}^{1} f(x) dx=2$ , $\int_{0}^{3} f(x) dx=6$ , find $\int_{-1}^{3} f(x) dx$ . a) 10 b) 12 c) 8 d) 14

Find the average rate of change of $f(x) = 2 \log_{3}{x} + 1$ over the interval $[1,27]$ .

Approximate the integral $\int_{2}^{14}(x^{2}+5) dx$ using a Riemann sum with 3 subintervals of length 4.

Find the tangent line to $f(t)=(e^{-t}+\sqrt{t})^{2}$ at $(1/2, f(1/2))$ . Choose from options a) to d).

If $y=(\cos(x^{7})+5x)^{15}$ , find $\frac{dy}{dt}$ .

Find the total reaction to a drug from $t=1$ to $t=10$ for $R^{\prime}(t)=\frac{6}{t}+\frac{4}{t^{3}}+e^{-2 t}$ . Round up.

Calculate the volume of the solid formed by revolving the area bounded by $x=y^{3/2}$ , $x=0$ , $y=2$ around the y-axis.

Find the time $x$ when the drug concentration $K(x)=\frac{4 x}{x^{2}+20}$ is at its maximum.

Find the derivative of the function $f(x)=(x^{3}+6x)^{4}$ . What is $\frac{d f(x)}{d x}$ ?

Calculate the integral $\int_{1}^{10}(x^{3}+4) dx$ using a Riemann sum with 3 subintervals and midpoints.

A bacteria culture grows proportionally. At 6:00 AM, there are 4,000 bacteria; at noon, there are 4,800. Find the count at midnight.
There will be about $\square$ bacteria at midnight.

Find $\int_{-2}^{5} f(x) d x$ given that $f$ is even and $\int_{0}^{2} f(x) dx=1$ , $\int_{0}^{5} f(x) dx=4$ .

Find $\frac{d f(x)}{d x}$ for $f(x)=(x^{3}+6x^{2})^{4}$ . Choose the correct option: a) b) c) d) e).

Approximate the integral $\int_{1}^{13}(x^{2}+5) dx$ using a Riemann sum with 3 subintervals of length 4.

Find the volume of the solid formed by rotating the area between $y = \sqrt{x}$ and $y = x^{2}$ around the x-axis.

Find $\frac{d y}{d t}$ for $y=\left(\sin \left(x^{8}\right)+6\right)^{6}$ . Choices include derivatives involving $x$ .

Bestimme den Grenzwert $\varlimsup_{n \to \infty} a_{n}$ für die Folge $a_{n}=5+\frac{4}{n}-\left(\frac{1}{n^{2}}+2\right)$ .

Find the total reaction from the $2^{\text{nd}}$ to the $10^{\text{th}}$ hour given $R^{\prime}(t)=\frac{6}{t}+\frac{4}{t^{3}}+e^{-2t}$ . Round up to the nearest whole number. Options: a) 7 b) 9 c) 12 d) 11

What time after administration does the drug concentration $K(x)=\frac{6x}{x^{2}+25}$ peak?

Find the tangent line to the curve $f(t)=\left(e^{-t}+\sqrt{t}\right)^{2}$ at the point $(2, f(2))$ .

Find the tangent line equation for $f(t)=\left(e^{-t}+\sqrt{t}\right)^{2}$ at $(3, f(3))$ .

Find the total reaction to a drug from the 2nd to the 8th hour given the rate $R^{\prime}(t)=\frac{4}{t}+\frac{3}{t^{3}}+e^{-2 t}$ . Round up your answer.

Find the derivative of $f(x)=(x^{3}+6x)^{4}$ . Which option is correct? a) b) c) d) e)

Approximate the integral $\int_{2}^{14}(x^{2}+3) dx$ using a Riemann sum with 3 subintervals of length 4.

Find the total reaction from hour 1 to hour 10 for $R^{\prime}(t)=\frac{4}{t}+\frac{3}{t^{3}}+e^{-2 t}$ . Round up.

Find $\frac{d y}{d t}$ for $y=\left(\tan \left(x^{5}\right)+5\right)^{6}$ . Choose the correct option.

Evaluate the integral $\int(\sin (x))^{12}(\cos (x)) d x$ and choose the correct answer from the options.

Approximate the integral $\int_{1}^{13}(x^{2}+5) dx$ using a Riemann sum with 3 subintervals of length 4. Choices: a) 488 b) 1160 c) 2879 d) 8591 e) None.

Approximate the integral $\int_{1}^{10}(x^{3}+4) dx$ using a Riemann sum with 3 subintervals of length 3. Choices: a) 1260 b) 1345 c) 2758.5 d) 4257 e) None.

Approximate the integral $\int_{2}^{14}(x^{2}+3) dx$ using a Riemann sum with 3 subintervals of length 4.

If $f$ is even and $\int_{0}^{3} f(x) dx=-2$ , $\int_{0}^{4} f(x) dx=3$ , find $\int_{-3}^{4} f(x) dx$ .

Find the derivative of the function $f(x)=(x^{3}+4x)^{3}$ . What is $\frac{d f(x)}{d x}$ ?

Find $\int_{-3}^{4} f(x) d x$ if $f$ is even, $\int_{0}^{3} f(x) d x=-2$ , and $\int_{0}^{4} f(x) d x=3$ .

Approximate the integral $\int_{2}^{11}(x^{3}+4)dx$ using 3 subintervals. Which partition is correct? a) b) c) d) e) None.

Find $\int_{-2}^{6} f(x) d x$ given that $f$ is even, $\int_{0}^{2} f(x) d x=1$ , and $\int_{0}^{6} f(x) d x=3$ .

Find the monkey's acceleration at time $t=3$ for the distance function $S(t)=t \sin (2 t)+t^{2}$ , rounding up results.

Approximate the change in drug concentration $C(x)=\frac{10 x}{9+x^{2}}$ from $x=0.5$ to $x=1.5$ .