Calculus

Problem 30801

Evaluate the right-endpoint Riemann sum for $f(x) = (1+k(\frac{9}{n}))^2$ over $[1, 10]$ . Find limits.

See Solution

Problem 30802

Find $f(x_k)$ , $f(x_k) \Delta x$ , the right-endpoint Riemann sum, and its limit as $n \to \infty$ .

See Solution

Problem 30803

Find when $A$ (initially $4500\, \mathrm{g}$ , $2\%$ daily decay) equals $B$ (initially $8500\, \mathrm{g}$ , $6\%$ decay).

See Solution

Problem 30804

Find the infimum and supremum of $f(t)=\frac{3 t^{2}}{1+t^{6}}$ , and determine if it has max/min values with their locations. Sketch the graph.

See Solution

Problem 30805

Given the piecewise function $f(x)$ , find values for $g(x) = \int_{-3}^{x} f(t) dt$ at $g(-5)$ , $g(-2)$ , $g(1)$ , $g(5)$ , and the max of $g(x)$ .

See Solution

Problem 30806

Find $c$ so that $y=\frac{1}{c x^{2}+1}$ solves $y' + 18 x y^{2} = 0$ .

See Solution

Problem 30807

Given $f(x)=-20 x^{3}+300 x^{2}+1000$ , determine where the maximum occurs and its value.

See Solution

Problem 30808

Find the limit as $k$ approaches 0 from the right of $(7 - 6 k^{-4})$ .

See Solution

Problem 30809

Evaluate the integral $\int_{0}^{8} f(x) dx$ for the piecewise function: $f(x)=2x-8$ if $0 \leq x<4$ and $f(x)=8-2x$ if $4 \leq x \leq 8$ .

See Solution

Problem 30810

Find the Riemann sum for $f(x)=\sqrt{x}-2$ on $[1, 6]$ with $n=5$ using midpoints. Round to six decimal points. $M_{5} =$

See Solution

Problem 30811

Evaluate the integral $\int_{0}^{2}(3-x^{2}) dx$ by finding $\Delta x$ and $x_{i}$ , then compute the integral.

See Solution

Problem 30812

Calculate the integral $\int_{0}^{10}|x-5| dx$ .

See Solution

Problem 30813

Find $A$ so that if $A x + b > 0$ , then $y = \ln(A x + B)$ solves $2 e^{y} y' = 7$ . What is $A$ ?

See Solution

Problem 30814

Berechnen Sie die mittlere Änderungsrate von $f$ in den Intervallen $[1 ; 3]$ , $[-3 ;-1]$ , $[-1 ; 2]$ für a) $f(x)=x^{2}$ , b) $f(x)=x^{3}+2 x$ , c) $f(x)=2 x^{2}-x$ .

See Solution

Problem 30815

Find the value of $\frac{dL}{dt}$ given the equation $kL(75 - L)$ .

See Solution

Problem 30816

Find the limit as $t$ approaches negative infinity for the expression $7 t^{-3} + 5$ .

See Solution

Problem 30817

Find the maximum $y$ -value of $g(x)=-\frac{3}{5} x^{3}-2 x^{2}+4 x+2$ for $-4<x<4$ , rounded to the nearest tenth.

See Solution

Problem 30818

Estimate the derivative $f^{\prime}(x)$ for $f(x)=6 \cdot 0.65^{x}$ using $h=0.001$ at $x=-3.25, 3, 3.75$ .

See Solution

Problem 30819

Calcula $\int t^{1} \, dt$ usando la fórmula $\int x^{n} \, dx = \frac{x^{n+1}}{n+1} + c$ .

See Solution

Problem 30820

How much to invest now to reach \ $8,000 in 25 years at a continuous interest rate of$ 2.9\%$?

See Solution

Problem 30821

Find the nonzero $x$ where the second derivative of $f(x)=9 x^{6}-3 x^{5}$ equals zero. Provide your answer as a decimal with three decimal places.

See Solution

Problem 30822

1. Bestimme die Tangentengleichung von $f_{a}(x)=a x(x-4)$ bei $x=4$ in Abhängigkeit von $a$ .
2. a) Finde die Normale von $f_{a}(x)=x^{2}-a x$ bei $P_{a}(a \mid 0)$ . b) Zeige, dass die Normale immer durch $Q(0 \mid 1)$ geht. c) Stelle die Ergebnisse grafisch dar.
3. a) Berechne den Flächeninhalt $A_{a}$ zwischen $f_{a}(x)=a x(x-4)$ und der $x$ -Achse. b) Finde $a$ für $A_{a}=48$ .

See Solution

Problem 30823

How long will it take for a $\$ 700$ investment at $12 \%$ continuous interest to triple? Round to the nearest tenth.

See Solution

Problem 30824

Bestimme die Gleichung der Normale von $f_{a}(x)=x^{2}-a x$ im Punkt $P_{a}(a \mid 0)$ und zeige, dass sie durch $Q(0 \mid 1)$ geht.

See Solution

Problem 30825

Solve the equation $s^{\prime \prime}(t)=\cos(t)-\sin(t)$ with $s(0)=2$ , $s^{\prime}(0)=5$ and find $s(\pi)$ .

See Solution

Problem 30826

Find the limit $\lim _{x \rightarrow \infty} G(x)$ for the antiderivative of $g(x)=e^{-3x}$ with $G(0)=11$ . Answer to three decimals.

See Solution

Problem 30827

$f(x)=\left\{\begin{array}{ll}x^{2} \sin \frac{1}{x} & ; x \neq 0 \\ 0 & ; x=0\end{array}\right.$ fonksiyonunun $(0,0)$ noktasındaki teğetin denklemi nedir? A) $x+y=1$ B) $y=2 x$ C) $y=x$ D) $y=1$ E) $y=0$

See Solution

Problem 30828

15. $y=\frac{1}{1-e^{x}}$ eğrisinin asimtotları hangi noktada kesişir? A) $(-1,1)$ B) $(1,1)$ C) $(0,1)$ D) $(1,0)$ E) $(0-1)$

See Solution

Problem 30829

$\lim _{x \rightarrow 1}(\sin x)^{\sec x}$ limitinin sonucu nedir? A) $\frac{1}{e}$ B) $c$ C) $e^{2}$ D) 0 E) 1

See Solution

Problem 30830

f(x) = \frac{|x|}{x} için x = 1'de türevlenebilirlik ve x = 0'da süreksizlik durumunu inceleyin.

See Solution

Problem 30831

Find the volume $V$ of the solid formed by rotating the region bounded by $y=x^{2}$ and $x=2$ about $x=2$ .

See Solution

Problem 30832

$\lim _{x \rightarrow \frac{\pi}{2}}(\sin x)^{\sec x}$ sonucunu bulun: A) $\frac{1}{e}$ B) $\mathrm{e}$ C) $e^{2}$ D) 0 E) 1

See Solution

Problem 30833

Determine the horizontal asymptotes of the function $f(x)=\frac{x-8}{3(x-9)(x-8)}$ .

See Solution

Problem 30834

Find the volume of the solid formed by rotating the region $R$ bounded by $y=x^{2}$ , the $x$ -axis, and $x=2$ about $x=2$ .

See Solution

Problem 30835

Find horizontal asymptotes of the function $f(x)=\frac{3 x^{2}+18 x+24}{x^{2}+2 x}$ .

See Solution

Problem 30836

Find horizontal asymptotes of $f(x)=\frac{x-8}{3(x-9)(x-8)}$ .

See Solution

Problem 30837

Which statement is not a Limit Law?
1. $\lim _{x \rightarrow c}[f(x)+g(x)]=\lim _{x \rightarrow c} f(x) + \lim _{x \rightarrow c} g(x)$
2. $\lim _{x \rightarrow c}[\alpha f(x)]=\alpha \lim _{x \rightarrow c} f(x)$
3. $\lim _{x \rightarrow c}[f(x) \cdot g(x)]=\left[\lim _{x \rightarrow c} f(x)\right] \cdot\left[\lim _{x \rightarrow c} g(x)\right]$
4. $\lim _{x \rightarrow a} f(x)+\lim _{x \rightarrow b} f(x)=\lim _{x \rightarrow(a+b)} f(x)$

See Solution

Problem 30838

Find the limit $\lim _{x \rightarrow \infty} f(x)$ for $f(x)=\frac{2 x^{2}+3 x}{(x+1)(x+2)}$ . What is the horizontal asymptote?

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Problem 30839

Estimate the integral $\int_{\pi / 4}^{3 \pi / 4} \sin^{2}(x) dx$ given $\frac{1}{2} \leq \sin^{2}(x) \leq 1$ . $\square \leq \int_{\pi / 4}^{3 \pi / 4} \sin^{2}(x) dx \leq \square$

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Problem 30840

True or False: If $f(x)$ is differentiable at $x=4$ , is $f(x)$ also continuous at $x=4$ ?

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Problem 30841

Prove that the derivative of $\sinh^{-1}(x)$ is $\frac{1}{\sqrt{1+x^2}}$ .

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Problem 30842

True or False: If $f(x)$ is a differentiable and increasing function, is $f^{\prime}(x) > 0$ for all $x$ ?

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Problem 30843

Find velocity and acceleration for $s=f(t)=5 t^{3}+4 t+9$ at time $t$ and specifically at $t=3$ seconds.

See Solution

Problem 30844

Find $y^{\prime}(1)$ using implicit differentiation for the equation $5 x^{2}+2 x+x y=1$ with $y(1)=-6$ .

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Problem 30845

Calculate the integral from $\frac{3 \pi}{2}$ to $2 \pi$ of $-4 \sin (x)$ .

See Solution

Problem 30846

Integrate the function: $\int 18 \cos (x) \, dx$

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Problem 30847

Find the integral of $x$ with respect to $x$ : $\int x \, dx$ .

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Problem 30848

Find the integral of the function: $\int \sqrt[3]{x^{7}} d x$

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Problem 30849

Find the integral of $x^{\frac{1}{2}}$ with respect to $x$ .

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Problem 30850

Find the derivative $f'(x)$ of $f(x)=-2x^3-4x+3$ using the limit definition, then find the second derivative $f''(x)$ .

See Solution

Problem 30851

Find the integral of the function: $\int(6 x^{2}-5 x+3) dx$ .

See Solution

Problem 30852

An object moves along the $x$ -axis with $x=(4.00 \mathrm{~m} / \mathrm{s}^{2}) t^{2}$ . Find positions at $t=3.10 \mathrm{~s}$ and $t=(3.10+\Delta t)$ . Also, find velocity limit as $\Delta t \to 0$ .

See Solution

Problem 30853

Evaluate the integral from 5 to 10 for the function $3x + 3$ : $\int_{5}^{10}(3 x+3) d x.$

See Solution

Problem 30854

Given the model $C(t)=-0.0034 t^{3}+0.097 t^{2}-0.351 t+12.4$ , find $C'(14)$ and $C'(18)$ to compare rates for 2004 and 2008.

See Solution

Problem 30855

Evaluate the integral from -2 to 1 for the piecewise function $f(x)=\{4 e^{x}$ if $x>0$ , $4-x$ if $x \leq 0\}$ .

See Solution

Problem 30856

Integrate: $\int\left(5 e^{x}-\frac{2}{x}\right) d x= ?$ Choose the correct answer: (A) $e^{5 x}-\ln |2|+C$ , (B) $5 e^{x}-2 \ln |x|+C$ , (C) $5 e^{x}-\ln |2|+C$ , (D) $e^{5 x}-2 \ln |x|+C$ .

See Solution

Problem 30857

Find $F(x)$ where $F(x)=\int_{-2}^{\cos (x)} 3 t d t$ .

See Solution

Problem 30858

Find the tangent line equation $y=m x+b$ for $h(x)=7-3 x^{3}$ at $(1,4)$ using $h^{\prime}(1)$ .

See Solution

Problem 30859

Find the derivative $F'(x)$ of the function $F(x)=\int_{-2}^{\cos (x)} 3t \, dt$ .

See Solution

Problem 30860

Find $R(56)$ and $R^{\prime}(56)$ for $R(t)=61.265 \cdot 0.954^{t}$ and interpret their values.

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Problem 30861

Find $F'(x)$ if $F(x)=\int_{0}^{x^{4}} \cos(t) dt$ .

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Problem 30862

Find the derivative $f^{\prime}(x)$ of the function $f(x)=5 \sqrt{x-8}$ using the limit definition.

See Solution

Problem 30863

Find $F'(x)$ for the function $F(x)=\int_{-2}^{2 x}(3 t^{2}+2 t) dt$ .

See Solution

Problem 30864

Find the salary in 1991 using $S(11)$ and interpret $S'(11)$ for its rate of change.

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Problem 30865

Find the limits of hyperbolic functions as $x \to \infty$ or $x \to -\infty$ : (a) $\tanh(x)$ , (b) $\tanh(x)$ , (c) $\sinh(x)$ , (d) $\sinh(x)$ , (e) $\operatorname{sech}(x)$ , (f) $\operatorname{coth}(x)$ , (g) $\operatorname{coth}(x)$ , (h) $\operatorname{coth}(x)$ , (i) $\operatorname{csch}(x)$ , (j) $\frac{\sinh(x)}{e^{x}}$ .

See Solution

Problem 30866

Find the area of intersection of the polar curves $r=4 \sin 2 \theta$ and $r=2$ .

See Solution

Problem 30867

Find the derivative $F'(x)$ of the function $F(x)=\int_{-2}^{2 x}(3 t^{2}+2 t) dt$ .

See Solution

Problem 30868

Find the derivative $f^{\prime}(x)$ of the function $f(x)=4-4 x^{2}$ using the limit definition.

See Solution

Problem 30869

An object moves along the $x$ axis: $x=3.40 t^{2}-2.00 t+3.00$ . Find speeds, accelerations, and when it is at rest.

See Solution

Problem 30870

Find the derivative $f^{\prime}(x)$ of the function $f(x)=\frac{5}{x}$ using the limit definition.

See Solution

Problem 30871

Find the derivative $F'(x)$ of the function defined by $F(x)=\int_{0}^{\sqrt{x}} 2 t dt$ for $x>0$ .

See Solution

Problem 30872

Find $g^{\prime}(2)$ for the function defined by the integral $g(x)=\int_{1}^{x}(3 t^{2}+4 t) dt$ .

See Solution

Problem 30873

An object moves along the $x$ axis with $x=3.40 t^{2}-2.00 t+3.00$ . Find speeds, accelerations, and rest time at given $t$ .

See Solution

Problem 30874

Find $F'(x)$ for the function defined by $F(x)=\int_{-2}^{2 x}(3 t^{2}+2 t) dt$ .

See Solution

Problem 30875

Find $g^{\prime}(9)$ for the function $g(x)=\int_{1}^{x} \sqrt{2t+7} \, dt$ .

See Solution

Problem 30876

A ball is thrown up with initial velocity $50 \mathrm{ft/s}$ . Find average velocity from $t=1$ for (i) 0.1s, (ii) 0.01s, (iii) 0.001s. Guess instantaneous velocity at $t=1$ .

See Solution

Problem 30877

A particle's position is $s(t)=2 t^{3}-24 t^{2}+42 t$ . Find its velocity at $t=0$ , when it stops, position at $t=16$ , and total distance from $t=0$ to $t=16$ .

See Solution

Problem 30878

Find $g^{\prime}(-3)$ for the function defined by the integral $g(x)=\int_{-8}^{x}(-2 t+4) d t$ .

See Solution

Problem 30879

Find the derivative of $f(x)=2 x^{2}+3 x+4$ at $x=4$ using the limit definition of a derivative.

See Solution

Problem 30880

Find $g^{\prime}(\pi)$ if $g(x)=\int_{0}^{x} \sqrt{5+4 \cos t} dt$ .

See Solution

Problem 30881

Find the value of $x$ where the tangent lines of $f(x)=3 e^{2 x}$ and $g(x)=6 x^{3}$ are parallel.

See Solution

Problem 30882

Solve the differential equation: $(6y - 2) \, dx + dy = 0$ .

See Solution

Problem 30883

Find $\frac{d^{2} y}{d x^{2}}$ if $y^{3}-x y=5$ .

See Solution

Problem 30884

Find the tangent line equation for $y=10-2x-3x^{2}$ at the point $(1,5)$ . $y=$

See Solution

Problem 30885

Find the derivative $f^{\prime}(a)$ for the function $f(x)=3 x^{2}-3 x-31$ .

See Solution

Problem 30886

Find the derivative $f^{\prime}(a)$ for the function $f(x)=3 x^{2}-3 x-3 i$ .

See Solution

Problem 30887

Solve the equation $x \sqrt{1-y} dx - \sqrt{1-x^{2}} dy = 0$ .

See Solution

Problem 30888

Solve the differential equation: $x \sqrt{1-y} \, dx - \sqrt{1-x^2} \, dy = 0$ .

See Solution

Problem 30889

Find the tangent line equation to $y=2 \sin x$ at $x=\frac{\pi}{3}$ .

See Solution

Problem 30890

A particle's position is $s(t)=2 t^{3}-24 t^{2}+42 t$ . Find velocity at $t=0$ , rest times, position at $t=16$ , and total distance 0 to 16.

See Solution

Problem 30891

Determine where the function $f(x) = 3x^4 + x^3 + 14$ is increasing.

See Solution

Problem 30892

Find all extrema of $f(x)=\sin(2x)$ in the interval $[-2\pi, 3\pi]$ .

See Solution

Problem 30893

Find the limit: $\lim _{x \rightarrow \infty} \frac{7 x+\ln 5 x}{9 x+\ln 3 x}$ .

See Solution

Problem 30894

Find the general antiderivative of $f(x)=(x+5)(5x-4)$ and verify by differentiation. Use $C$ for the constant.

See Solution

Problem 30895

Determine if the derivative $f^{\prime}(0)$ exists for $f(x)=x \sin \frac{-2}{x}$ if $x \neq 0$ , $0$ if $x=0$ . Answer Yes or No: [?/Yes/No]

See Solution

Problem 30896

Determine if the derivative $f^{\prime}(0)$ exists for the function $f(x)=3 x^{3} \sin \frac{1}{x}$ if $x \neq 0$ and $f(0)=0$ . Answer Yes or No: [?/Yes/No]

See Solution

Problem 30897

Jackson invested \$320 at a 3.2% continuous interest rate. How long until the account reaches \$410? Round to the nearest tenth.

See Solution

Problem 30898

A particle's position is $s(t)=2 t^{3}-27 t^{2}+108 t$ . Find velocity at $t=0$ , when it stops, position at $t=18$ , and total distance from $t=0$ to $t=18$ .

See Solution

Problem 30899

Find the general antiderivative of $f(x)=5 x^{1/4}-7 x^{3/4}$ and verify by differentiation using constant $C$ .

See Solution

Problem 30900

Find the function $f(x)$ and the number $a$ such that $\lim _{h \rightarrow 0} \frac{(3+h)^{2}-9}{h}$ defines the derivative.

See Solution

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Calculus

Problem 30801

Evaluate the right-endpoint Riemann sum for f(x)=(1+k(9n))2f(x) = (1+k(\frac{9}{n}))^2f(x)=(1+k(n9​))2 over [1,10][1, 10][1,10]. Find limits.

Problem 30802

Find f(xk)f(x_k)f(xk​), f(xk)Δxf(x_k) \Delta xf(xk​)Δx, the right-endpoint Riemann sum, and its limit as n→∞n \to \inftyn→∞.

Problem 30803

Find when AAA (initially 4500 g4500\, \mathrm{g}4500g, 2%2\%2% daily decay) equals BBB (initially 8500 g8500\, \mathrm{g}8500g, 6%6\%6% decay).

Problem 30804

Find the infimum and supremum of f(t)=3t21+t6f(t)=\frac{3 t^{2}}{1+t^{6}}f(t)=1+t63t2​, and determine if it has max/min values with their locations. Sketch the graph.

Problem 30805

Given the piecewise function f(x)f(x)f(x), find values for g(x)=∫−3xf(t)dtg(x) = \int_{-3}^{x} f(t) dtg(x)=∫−3x​f(t)dt at g(−5)g(-5)g(−5), g(−2)g(-2)g(−2), g(1)g(1)g(1), g(5)g(5)g(5), and the max of g(x)g(x)g(x).

Problem 30806

Find ccc so that y=1cx2+1y=\frac{1}{c x^{2}+1}y=cx2+11​ solves y′+18xy2=0y' + 18 x y^{2} = 0y′+18xy2=0.

Problem 30807

Given f(x)=−20x3+300x2+1000f(x)=-20 x^{3}+300 x^{2}+1000f(x)=−20x3+300x2+1000, determine where the maximum occurs and its value.

Problem 30808

Find the limit as kkk approaches 0 from the right of (7−6k−4)(7 - 6 k^{-4})(7−6k−4).

Problem 30809

Evaluate the integral ∫08f(x)dx\int_{0}^{8} f(x) dx∫08​f(x)dx for the piecewise function: f(x)=2x−8f(x)=2x-8f(x)=2x−8 if 0≤x<40 \leq x<40≤x<4 and f(x)=8−2xf(x)=8-2xf(x)=8−2x if 4≤x≤84 \leq x \leq 84≤x≤8.

Problem 30810

Find the Riemann sum for f(x)=x−2f(x)=\sqrt{x}-2f(x)=x​−2 on [1,6][1, 6][1,6] with n=5n=5n=5 using midpoints. Round to six decimal points. M5= M_{5} = M5​=

Problem 30811

Evaluate the integral ∫02(3−x2)dx\int_{0}^{2}(3-x^{2}) dx∫02​(3−x2)dx by finding Δx\Delta xΔx and xix_{i}xi​, then compute the integral.

Problem 30812

Calculate the integral ∫010∣x−5∣dx\int_{0}^{10}|x-5| dx∫010​∣x−5∣dx.

Problem 30813

Find AAA so that if Ax+b>0A x + b > 0Ax+b>0, then y=ln⁡(Ax+B)y = \ln(A x + B)y=ln(Ax+B) solves 2eyy′=72 e^{y} y' = 72eyy′=7. What is AAA?

Problem 30814

Berechnen Sie die mittlere Änderungsrate von fff in den Intervallen [1;3][1 ; 3][1;3], [−3;−1][-3 ;-1][−3;−1], [−1;2][-1 ; 2][−1;2] für a) f(x)=x2f(x)=x^{2}f(x)=x2, b) f(x)=x3+2xf(x)=x^{3}+2 xf(x)=x3+2x, c) f(x)=2x2−xf(x)=2 x^{2}-xf(x)=2x2−x.

Problem 30815

Find the value of dLdt\frac{dL}{dt}dtdL​ given the equation kL(75−L)kL(75 - L)kL(75−L).

Problem 30816

Find the limit as ttt approaches negative infinity for the expression 7t−3+57 t^{-3} + 57t−3+5.

Problem 30817

Find the maximum yyy-value of g(x)=−35x3−2x2+4x+2g(x)=-\frac{3}{5} x^{3}-2 x^{2}+4 x+2g(x)=−53​x3−2x2+4x+2 for −4<x<4-4<x<4−4<x<4, rounded to the nearest tenth.

Problem 30818

Estimate the derivative f′(x)f^{\prime}(x)f′(x) for f(x)=6⋅0.65xf(x)=6 \cdot 0.65^{x}f(x)=6⋅0.65x using h=0.001h=0.001h=0.001 at x=−3.25,3,3.75x=-3.25, 3, 3.75x=−3.25,3,3.75.

Problem 30819

Calcula ∫t1 dt\int t^{1} \, dt∫t1dt usando la fórmula ∫xn dx=xn+1n+1+c\int x^{n} \, dx = \frac{x^{n+1}}{n+1} + c∫xndx=n+1xn+1​+c.

Problem 30820

How much to invest now to reach \8,000in25yearsatacontinuousinterestrateof8,000 in 25 years at a continuous interest rate of 8,000in25yearsatacontinuousinterestrateof2.9\%$?

Problem 30821

Find the nonzero xxx where the second derivative of f(x)=9x6−3x5f(x)=9 x^{6}-3 x^{5}f(x)=9x6−3x5 equals zero. Provide your answer as a decimal with three decimal places.

Problem 30822

Problem 30823

How long will it take for a $700\$ 700$700 investment at 12%12 \%12% continuous interest to triple? Round to the nearest tenth.

Problem 30824

Bestimme die Gleichung der Normale von fa(x)=x2−axf_{a}(x)=x^{2}-a xfa​(x)=x2−ax im Punkt Pa(a∣0)P_{a}(a \mid 0)Pa​(a∣0) und zeige, dass sie durch Q(0∣1)Q(0 \mid 1)Q(0∣1) geht.

Problem 30825

Solve the equation s′′(t)=cos⁡(t)−sin⁡(t)s^{\prime \prime}(t)=\cos(t)-\sin(t)s′′(t)=cos(t)−sin(t) with s(0)=2s(0)=2s(0)=2, s′(0)=5s^{\prime}(0)=5s′(0)=5 and find s(π)s(\pi)s(π).

Problem 30826

Find the limit lim⁡x→∞G(x)\lim _{x \rightarrow \infty} G(x)limx→∞​G(x) for the antiderivative of g(x)=e−3xg(x)=e^{-3x}g(x)=e−3x with G(0)=11G(0)=11G(0)=11. Answer to three decimals.

Problem 30827

Problem 30828

15. y=11−exy=\frac{1}{1-e^{x}}y=1−ex1​ eğrisinin asimtotları hangi noktada kesişir? A) (−1,1)(-1,1)(−1,1) B) (1,1)(1,1)(1,1) C) (0,1)(0,1)(0,1) D) (1,0)(1,0)(1,0) E) (0−1)(0-1)(0−1)

Problem 30829

lim⁡x→1(sin⁡x)sec⁡x\lim _{x \rightarrow 1}(\sin x)^{\sec x}limx→1​(sinx)secx limitinin sonucu nedir? A) 1e\frac{1}{e}e1​ B) ccc C) e2e^{2}e2 D) 0 E) 1

Problem 30830

f(x) = \frac{|x|}{x} için x = 1'de türevlenebilirlik ve x = 0'da süreksizlik durumunu inceleyin.

Problem 30831

Find the volume VVV of the solid formed by rotating the region bounded by y=x2y=x^{2}y=x2 and x=2x=2x=2 about x=2x=2x=2.

Problem 30832

lim⁡x→π2(sin⁡x)sec⁡x\lim _{x \rightarrow \frac{\pi}{2}}(\sin x)^{\sec x}limx→2π​​(sinx)secx sonucunu bulun: A) 1e\frac{1}{e}e1​ B) e\mathrm{e}e C) e2e^{2}e2 D) 0 E) 1

Problem 30833

Determine the horizontal asymptotes of the function f(x)=x−83(x−9)(x−8)f(x)=\frac{x-8}{3(x-9)(x-8)}f(x)=3(x−9)(x−8)x−8​.

Problem 30834

Find the volume of the solid formed by rotating the region RRR bounded by y=x2y=x^{2}y=x2, the xxx-axis, and x=2x=2x=2 about x=2x=2x=2.

Problem 30835

Find horizontal asymptotes of the function f(x)=3x2+18x+24x2+2xf(x)=\frac{3 x^{2}+18 x+24}{x^{2}+2 x}f(x)=x2+2x3x2+18x+24​.

Problem 30836

Find horizontal asymptotes of f(x)=x−83(x−9)(x−8)f(x)=\frac{x-8}{3(x-9)(x-8)}f(x)=3(x−9)(x−8)x−8​.

Problem 30837

Problem 30838

Find the limit lim⁡x→∞f(x)\lim _{x \rightarrow \infty} f(x)limx→∞​f(x) for f(x)=2x2+3x(x+1)(x+2)f(x)=\frac{2 x^{2}+3 x}{(x+1)(x+2)}f(x)=(x+1)(x+2)2x2+3x​. What is the horizontal asymptote?

Problem 30839

Problem 30840

True or False: If f(x)f(x)f(x) is differentiable at x=4x=4x=4, is f(x)f(x)f(x) also continuous at x=4x=4x=4?

Problem 30841

Prove that the derivative of sinh⁡−1(x)\sinh^{-1}(x)sinh−1(x) is 11+x2\frac{1}{\sqrt{1+x^2}}1+x2​1​.

Problem 30842

Evaluate the right-endpoint Riemann sum for $f(x) = (1+k(\frac{9}{n}))^2$ over $[1, 10]$ . Find limits.

Find $f(x_k)$ , $f(x_k) \Delta x$ , the right-endpoint Riemann sum, and its limit as $n \to \infty$ .

Find when $A$ (initially $4500\, \mathrm{g}$ , $2\%$ daily decay) equals $B$ (initially $8500\, \mathrm{g}$ , $6\%$ decay).

Find the infimum and supremum of $f(t)=\frac{3 t^{2}}{1+t^{6}}$ , and determine if it has max/min values with their locations. Sketch the graph.

Given the piecewise function $f(x)$ , find values for $g(x) = \int_{-3}^{x} f(t) dt$ at $g(-5)$ , $g(-2)$ , $g(1)$ , $g(5)$ , and the max of $g(x)$ .

Find $c$ so that $y=\frac{1}{c x^{2}+1}$ solves $y' + 18 x y^{2} = 0$ .

Given $f(x)=-20 x^{3}+300 x^{2}+1000$ , determine where the maximum occurs and its value.

Find the limit as $k$ approaches 0 from the right of $(7 - 6 k^{-4})$ .

Evaluate the integral $\int_{0}^{8} f(x) dx$ for the piecewise function: $f(x)=2x-8$ if $0 \leq x<4$ and $f(x)=8-2x$ if $4 \leq x \leq 8$ .

Find the Riemann sum for $f(x)=\sqrt{x}-2$ on $[1, 6]$ with $n=5$ using midpoints. Round to six decimal points. $M_{5} =$

Evaluate the integral $\int_{0}^{2}(3-x^{2}) dx$ by finding $\Delta x$ and $x_{i}$ , then compute the integral.

Calculate the integral $\int_{0}^{10}|x-5| dx$ .

Find $A$ so that if $A x + b > 0$ , then $y = \ln(A x + B)$ solves $2 e^{y} y' = 7$ . What is $A$ ?

Berechnen Sie die mittlere Änderungsrate von $f$ in den Intervallen $[1 ; 3]$ , $[-3 ;-1]$ , $[-1 ; 2]$ für a) $f(x)=x^{2}$ , b) $f(x)=x^{3}+2 x$ , c) $f(x)=2 x^{2}-x$ .

Find the value of $\frac{dL}{dt}$ given the equation $kL(75 - L)$ .

Find the limit as $t$ approaches negative infinity for the expression $7 t^{-3} + 5$ .

Find the maximum $y$ -value of $g(x)=-\frac{3}{5} x^{3}-2 x^{2}+4 x+2$ for $-4<x<4$ , rounded to the nearest tenth.

Estimate the derivative $f^{\prime}(x)$ for $f(x)=6 \cdot 0.65^{x}$ using $h=0.001$ at $x=-3.25, 3, 3.75$ .

Calcula $\int t^{1} \, dt$ usando la fórmula $\int x^{n} \, dx = \frac{x^{n+1}}{n+1} + c$ .

How much to invest now to reach \ $8,000 in 25 years at a continuous interest rate of$ 2.9\%$?

Find the nonzero $x$ where the second derivative of $f(x)=9 x^{6}-3 x^{5}$ equals zero. Provide your answer as a decimal with three decimal places.

How long will it take for a $\$ 700$ investment at $12 \%$ continuous interest to triple? Round to the nearest tenth.

Bestimme die Gleichung der Normale von $f_{a}(x)=x^{2}-a x$ im Punkt $P_{a}(a \mid 0)$ und zeige, dass sie durch $Q(0 \mid 1)$ geht.

Solve the equation $s^{\prime \prime}(t)=\cos(t)-\sin(t)$ with $s(0)=2$ , $s^{\prime}(0)=5$ and find $s(\pi)$ .

Find the limit $\lim _{x \rightarrow \infty} G(x)$ for the antiderivative of $g(x)=e^{-3x}$ with $G(0)=11$ . Answer to three decimals.

15. $y=\frac{1}{1-e^{x}}$ eğrisinin asimtotları hangi noktada kesişir? A) $(-1,1)$ B) $(1,1)$ C) $(0,1)$ D) $(1,0)$ E) $(0-1)$

$\lim _{x \rightarrow 1}(\sin x)^{\sec x}$ limitinin sonucu nedir? A) $\frac{1}{e}$ B) $c$ C) $e^{2}$ D) 0 E) 1

Find the volume $V$ of the solid formed by rotating the region bounded by $y=x^{2}$ and $x=2$ about $x=2$ .

$\lim _{x \rightarrow \frac{\pi}{2}}(\sin x)^{\sec x}$ sonucunu bulun: A) $\frac{1}{e}$ B) $\mathrm{e}$ C) $e^{2}$ D) 0 E) 1

Determine the horizontal asymptotes of the function $f(x)=\frac{x-8}{3(x-9)(x-8)}$ .

Find the volume of the solid formed by rotating the region $R$ bounded by $y=x^{2}$ , the $x$ -axis, and $x=2$ about $x=2$ .

Find horizontal asymptotes of the function $f(x)=\frac{3 x^{2}+18 x+24}{x^{2}+2 x}$ .

Find horizontal asymptotes of $f(x)=\frac{x-8}{3(x-9)(x-8)}$ .

Find the limit $\lim _{x \rightarrow \infty} f(x)$ for $f(x)=\frac{2 x^{2}+3 x}{(x+1)(x+2)}$ . What is the horizontal asymptote?

True or False: If $f(x)$ is differentiable at $x=4$ , is $f(x)$ also continuous at $x=4$ ?

Prove that the derivative of $\sinh^{-1}(x)$ is $\frac{1}{\sqrt{1+x^2}}$ .

True or False: If $f(x)$ is a differentiable and increasing function, is $f^{\prime}(x) > 0$ for all $x$ ?

Find velocity and acceleration for $s=f(t)=5 t^{3}+4 t+9$ at time $t$ and specifically at $t=3$ seconds.

Find $y^{\prime}(1)$ using implicit differentiation for the equation $5 x^{2}+2 x+x y=1$ with $y(1)=-6$ .

Calculate the integral from $\frac{3 \pi}{2}$ to $2 \pi$ of $-4 \sin (x)$ .

Integrate the function: $\int 18 \cos (x) \, dx$

Find the integral of $x$ with respect to $x$ : $\int x \, dx$ .

Find the integral of the function: $\int \sqrt[3]{x^{7}} d x$

Find the integral of $x^{\frac{1}{2}}$ with respect to $x$ .

Find the derivative $f'(x)$ of $f(x)=-2x^3-4x+3$ using the limit definition, then find the second derivative $f''(x)$ .

Find the integral of the function: $\int(6 x^{2}-5 x+3) dx$ .

An object moves along the $x$ -axis with $x=(4.00 \mathrm{~m} / \mathrm{s}^{2}) t^{2}$ . Find positions at $t=3.10 \mathrm{~s}$ and $t=(3.10+\Delta t)$ . Also, find velocity limit as $\Delta t \to 0$ .

Evaluate the integral from 5 to 10 for the function $3x + 3$ : $\int_{5}^{10}(3 x+3) d x.$

Given the model $C(t)=-0.0034 t^{3}+0.097 t^{2}-0.351 t+12.4$ , find $C'(14)$ and $C'(18)$ to compare rates for 2004 and 2008.

Evaluate the integral from -2 to 1 for the piecewise function $f(x)=\{4 e^{x}$ if $x>0$ , $4-x$ if $x \leq 0\}$ .

Find $F(x)$ where $F(x)=\int_{-2}^{\cos (x)} 3 t d t$ .

Find the tangent line equation $y=m x+b$ for $h(x)=7-3 x^{3}$ at $(1,4)$ using $h^{\prime}(1)$ .

Find the derivative $F'(x)$ of the function $F(x)=\int_{-2}^{\cos (x)} 3t \, dt$ .

Find $R(56)$ and $R^{\prime}(56)$ for $R(t)=61.265 \cdot 0.954^{t}$ and interpret their values.

Find $F'(x)$ if $F(x)=\int_{0}^{x^{4}} \cos(t) dt$ .

Find the derivative $f^{\prime}(x)$ of the function $f(x)=5 \sqrt{x-8}$ using the limit definition.

Find $F'(x)$ for the function $F(x)=\int_{-2}^{2 x}(3 t^{2}+2 t) dt$ .

Find the salary in 1991 using $S(11)$ and interpret $S'(11)$ for its rate of change.

Find the area of intersection of the polar curves $r=4 \sin 2 \theta$ and $r=2$ .

Find the derivative $F'(x)$ of the function $F(x)=\int_{-2}^{2 x}(3 t^{2}+2 t) dt$ .

Find the derivative $f^{\prime}(x)$ of the function $f(x)=4-4 x^{2}$ using the limit definition.

An object moves along the $x$ axis: $x=3.40 t^{2}-2.00 t+3.00$ . Find speeds, accelerations, and when it is at rest.

Find the derivative $f^{\prime}(x)$ of the function $f(x)=\frac{5}{x}$ using the limit definition.

Find the derivative $F'(x)$ of the function defined by $F(x)=\int_{0}^{\sqrt{x}} 2 t dt$ for $x>0$ .

Find $g^{\prime}(2)$ for the function defined by the integral $g(x)=\int_{1}^{x}(3 t^{2}+4 t) dt$ .

An object moves along the $x$ axis with $x=3.40 t^{2}-2.00 t+3.00$ . Find speeds, accelerations, and rest time at given $t$ .

Find $F'(x)$ for the function defined by $F(x)=\int_{-2}^{2 x}(3 t^{2}+2 t) dt$ .