Calculus Archive: Questions from September 21, 2022
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Evaluate i. \( \int_{0}^{1}\left(2 x^{2}+1\right)\left(2 x^{3}+3 x+4\right)^{1 / 2} \mathrm{~d} x \) ii. \( \int_{0}^{\frac{\pi}{2}} \frac{\cos (x)}{(4+\sin (x))^{2}} \mathrm{~d} x \) iii. \( \int_{0}1 answer -
#42 please
41-44 Find the exact length of the curve. 41. \( x=1+3 t^{2}, \quad y=4+2 t^{3}, \quad 0 \leqslant t \leqslant 1 \) 42. \( x=e^{t}-t, \quad y=4 e^{t / 2}, \quad 0 \leqslant t \leqslant 2 \) 43. \( x=t1 answer -
If \( y^{\prime \prime}=\frac{1}{(x+1)^{2}}, y(0)=2, y^{\prime}(0)=1^{\text {then }} y^{\prime}= \) and \( y= \)1 answer -
if \( y=\frac{\cos x}{x} \), then \( y^{\prime}= \) and \( y^{\prime \prime}= \) Hence, \( x y^{\prime \prime}+2 y^{\prime}=1 \)2 answers -
0 answers
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Find \( y^{\prime} \) and \( y^{\prime \prime} \). \[ y=x^{2} \ln (9 x) \] \[ y^{2}= \] \[ y^{n}= \] 4.16/8.33 Points] Find \( y^{\prime} \) and \( y^{\prime \prime} \). \[ \begin{array}{l} y=\ln (\se2 answers -
2 answers
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9. Solve the initial value problem. \( y^{\prime}+y=f(x), y(0)=1 \), where \[ f(x)=\left\{\begin{array}{ll} 0, & \text { if } 0 \leq x2 answers -
A. ving to another question will save this response. ?uest 14 isificar la serie como absolutamente o condicionalmente convergente \( \sum_{n=1}^{\infty} \frac{(-1)^{n}}{n^{5}} \) Diverge Converge cond1 answer -
Use the Laplace transform to solve the initial value problem. Obtain \( Y(s) \) and \( y(t) \) \[ \begin{array}{ll} \text { 1.- } y^{\prime}+4 y=e^{-4 t}, & y(0)=2 \\ \text { 2.- } y^{\prime}-y=1+t e^1 answer -
Differentiate the function. \[ y=\sqrt{x}(x-8) \] \[ y^{\prime}= \] [-/0.25 Points] Differentiate the function. \[ y=7 e^{x}+\frac{4}{\sqrt[3]{x}} \] \[ y^{\prime}= \]1 answer -
1. Para la serie de potencias \( \sum_{n=0}^{\infty} \frac{(x+4)^{n}}{n^{5}} \) determina a. El centro b. El radio de convergencia c. El intervalo de convergencia 2. Determine una serie de potencias p1 answer -
Use the Laplace transform to solve the initial value problem. Obtain \( Y(s) \) and \( y(t) \) 1. \( -y^{\prime}+4 y=e^{-4 t}, \quad y(0)=2 \) 2. \( -y^{\prime}-y=1+t e^{t}, \quad y(0)=0 \) 3.- \( y^{2 answers -
Use the Laplace transform to solve the initial value problem. Obtain \( Y(s) \) and \( y(t) \) 1. \( -y^{\prime}+4 y=e^{-4 t}, \quad y(0)=2 \) 2. \( -y^{\prime}-y=1+t e^{t}, \quad y(0)=0 \) 3.- \( y^{2 answers -
evaluate each expression please
\( \sin ^{-1}\left(\sin \frac{52 \pi}{19}\right) \) \( \cos ^{-1}\left(\cos \left(-\frac{\pi}{17}\right)\right) \)2 answers -
find y'
(d) \( 2^{x y}=x^{2} y^{2} \) (e) \( \sin \left(x^{3}+y^{3}\right)=\tan \left(x^{3} y^{3}\right) \)2 answers -
2 answers
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Practice your differentiation formulas by differentiating the following functions.
\[ y=14 \] Elija una coincidencia \( y=x^{4} \) Elija una coincidencia \( y=5 x^{3} \) Elija una coincidencia \( y=3 x^{2}+4 x \) Elija una coincidencia \( y=\left(x^{2}-2\right)(x+4) \) Elija una coi2 answers -
\[ f(x)=\cos (\pi x), \quad\left[0, \frac{1}{2}\right] \] minimum \( \quad(x, y)=( \) maximum \( \quad(x, y)=( \)2 answers -
2 answers
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2 answers
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If \( f(x)=\cos (x) \) and \( g(x)=x+\frac{\pi}{4} \) what is the range of \( (f \circ g)(x) ? \) a) \( \{y \mid-1 \leq y \leq 1, y \in R\} \) b) \( \left\{y \mid 0 \leq y \leq \frac{\pi}{4}, y \in R\1 answer -
D \( y=\sqrt[5]{-x^{3}-4 x} \) (1) \( y=(3 x-1)\left(-4 x^{2}+1\right)^{-2} \) 3) \( y=\left(\frac{e^{x}-\cos x}{\tan x+\sin x}\right)^{4} \) 1) \( y=\left(\sec \left(2 x^{4}\right)\right)^{3} \) \( y1 answer -
Id the domain of the given function: \( f(x, y)=\frac{5}{2 x^{2}+3 y^{2}} \). \( \{(x, y) \mid x \neq-3 / 2 y\} \) \( \{(x, y) \mid(x, y) \neq(0,0)\} \) \( \{(x, y) \mid x \neq-2 / 3 y\} \) \( \{(x, y2 answers -
Find the domain of the given function: \( f(x, y)=\frac{6}{\sqrt{y-5 x^{2}}} \). a) \( \quad\left\{(x, y) \mid \mathrm{y} \leq 5 \mathrm{x}^{2}\right\} \) b) \( \quad\left\{(x, y) \mid \mathrm{y}>5 \m2 answers -
Find the domain of the given function: \( f(x, y, z)=\mathrm{e}^{\sqrt{4-25\left(x^{2}+y^{2}+z^{2}\right)}} \). a) \( \quad\left\{(x, y, z) \mathrm{I} \quad x^{2}+y^{2}+z^{2} \leq^{25} / 4\right\} \)2 answers -
2 answers
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Express the integral \( \iiint_{E} f(x, y, z) d V \) as an iterated integral in six different ways, where \( \mathrm{E} \) is the solid bounded by \( z=0, z=8 y \) and \( x^{2}=16-y \). 1. \( \int_{a}2 answers -
Express the integral \( \iiint_{E} f(x, y, z) d V \) as an iterated integral in six different ways, where \( \mathrm{E} \) is the solid bounded by \( z=0, x=0, z=y-5 x \) and \( y=10 \). 1. \( \int_{a0 answers -
Find the domain of the given function: \( f(x, y, z)=\frac{-z^{2}}{\sqrt{9 x^{2}-4 y^{2}}} \). a) \( \left\{(x, y, z) \mid \quad x \geq \frac{2}{3} y\right\} \) b) \( \left\{(x, y, z)|| x\left|\geq^{22 answers -
Evaluate the integral. \[ \begin{array}{l} \int 11 \tan ^{5} x \sec ^{4} x d x \\ \int 11 \tan ^{5} x \sec ^{4} x d x= \end{array} \]2 answers -
#30 please
Finding a Derivative In Exercises 9-34, find the derivative of the function. 9. \( y=(2 x-7)^{3} \) 10. \( y=5\left(2-x^{3}\right)^{4} \) 11. \( g(x)=3(4-9 x)^{5 / 6} \) 12. \( f(t)=(9 t+2)^{2 / 3} \)2 answers -
36 , 38 & 46 please!
Finding a Derivative of a Trigonometric Function In Exercises 35-54, find the derivative of the trigonometric function. 35. \( y=\cos 4 x \) 36. \( y=\sin \pi x \) 37. \( g(x)=5 \tan 3 x \) 38. \( h(x2 answers -
1 answer