Calculus Archive: Questions from November 08, 2022
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In Problems \( 1 \& 2 \), find \( f_{x} \) and \( f_{y} \). 1. \( f(x, y)=e^{2 x-y} \) 2. \( f(x, y)=y \ln (x y) \)2 answers -
Differentiate the following functions with respect to \( x \). a) \( y=(1+2 x)^{14} \) b) \( y=\left(x^{2}+89\right)^{2} \) c) \( y=\ln (3 x+1) \) d) \( y=\sin ^{2} x \) e) \( y=\sin ^{3}\left(\frac{\2 answers -
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Please solve all of these questions 57, 63, 65, 67, 69, 71, 73 and 76 asap 🙏🙏
\( y=\ln \left(x^{2}+y^{2}\right) \) 63-78 Find the derivative of the function. Simplify where possible. 63. \( f(x)=\sin ^{-1}(5 x) \) 64. \( g(x)=\sec ^{-1}\left(e^{x}\right) \) 65. \( y=\tan ^{-1}2 answers -
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Evaluate the triple integral. \[ \iiint_{E} y d V \text {, where } E=\{(x, y, z) \mid 0 \leq x \leq 6,0 \leq y \leq x, x-y \leq z \leq x+y\} \]2 answers -
Consider the region bounded by the following 3 functions A) Determine the area that region D occupies. B) Determine the volume of the solid in the area D
Considera la región acotada por las siguientes tres funciones: \[ f(x)=x^{2} ; g(x)=\sqrt[3]{x} ; h(x)=2-x \] a) Determina el área-que ocypa la región \( D \) b) Determina el volumen del sólido qu2 answers -
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Derivatives of Exponential Functions (Ma-220) \[ y=5 e^{7 x} \] \[ y=\frac{e^{x}}{2 x} \] \[ y=\sqrt{1-e^{x}} \] \[ y=\frac{x}{e^{x}+1} \] \[ y=e^{1+x^{3}} \] \[ y=e^{\sqrt[3]{x}} \] \[ y=x e^{\frac{12 answers -
Find \( \frac{d y}{d x} \) : \[ y=\frac{3 x^{2}+9}{2 x+3} \] \[ y=3 x e^{\sqrt{x}} \] \[ y=\sec \left(\tan \left(x^{3}\right)\right) \] \[ y=x^{2} \log _{3}(2-3 x) \]2 answers -
Find the divergence of the vector field \( \mathbf{F} \). \[ \mathbf{F}(x, y, z)=\ln \left(9 x^{2}+2 y^{2}\right) \mathbf{i}+18 x y \mathbf{j}+\ln \left(2 y^{2}+7 z^{2}\right) \mathbf{k} \] \( \operat2 answers -
PLEASE SHOW WORK
Find the stationary values of the following functions: (a) \( y=3 x_{1}^{2}+2 x_{2}^{2}+5 \) (b) \( y=2 x_{1}^{2}-4 x_{2}^{2}+1 \) (g) \( y=\left(x_{1}^{2}+x_{2}^{4}+x_{3}^{6}\right)^{2} \) (h) \( y=2 answers -
\( 0 \leq \rho \leq 6,0 \leq 0 \leq 0 \) orical coordinates by Describe the solidE in rectangular coorinato. Describe the solid \( E \) in rectangular coordinates. \[ \begin{array}{c} E=\left\{(x, y,2 answers -
If \( \iint_{R} f(x, y) d A=\int_{0}^{2 \pi} \int_{0}^{2} \frac{1}{r} d r d \theta \), find the integrand \( f(x, y) \). \[ f(x, y)=\frac{1}{\sqrt{x^{2}+3}} \] \( f(x, y)=1 \) \( f(x, y)=\frac{1}{x^{22 answers -
Do 22
21-24 Evaluate the line integral \( \int_{C} \mathbf{F} \cdot d \mathbf{r} \), where \( C \) is given by the vector function \( \mathbf{r}(t) \). 21. \( \mathbf{F}(x, y)=x y^{2} \mathbf{i}-x^{2} \math2 answers -
Which function satisfies the differential equation \( y^{\prime \prime}=4 y \) ? \[ \begin{array}{l} y=4 e^{x} \\ y=e^{2 x}-\sin (2 x) \\ y=e^{-2 x} \\ y=e^{4 x} \end{array} \]2 answers -
Find the gradient vector field \( (\vec{F}(x, y, z)) \) of \( f(x, y, z)=z \cos \left(\frac{3 x}{y}\right) \). \[ \vec{F}(x, y, z)=\langle \]2 answers -
Find the gradient vector field \( (\vec{F}(x, y, z)) \) of \( f(x, y, z)=z^{2} \sin (5 x y) \). \[ \vec{F}(x, y, z)= \]2 answers -
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Evaluate \( \iiint_{\mathcal{B}} f(x, y, z) d V \) for the specified function \( f \) and \( \mathcal{B}: \) \[ f(x, y, z)=\frac{z}{x} \quad 2 \leq x \leq 14,0 \leq y \leq 8,0 \leq z \leq 2 \] \[ \iii2 answers -
Solve usingLaplace transform \[ \begin{array}{l} y^{\prime \prime}+2 y=\sin (2 t) \\ y(0)=0 \\ y^{\prime}(0)=0 \end{array} \]2 answers -
Numbers 11, 13, 15, 17, 19, or 21 whichever ones you could answer, especially explaining concavity. Sketch the curve, find a) Domain, b) X and Y intercepts d) assymtotes e) increasing ans decreasing i
1-40 Use the guidelines of this section to sketch the curve. 1. \( y=x^{3}+3 x^{2} \) 2. \( y=2 x^{3}-12 x^{2}+18 x \) 3. \( y=x^{4}-4 x \) 4. \( y=x^{4}-8 x^{2}+8 \) 5. \( y=x(x-4)^{3} \) 6. \( y=x^{2 answers -
Verify the identity. \[ \begin{array}{l} \frac{1-\cot ^{2} x}{1+\cot ^{2} x}+1=2 \sin ^{2} x \\ \frac{\sin \theta}{1+\cos \theta}+\frac{1+\cos \theta}{\sin \theta}=2 \csc \theta \\ 2 \cot \theta \cot2 answers -
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3) Calcula el volumen del solido que se genera cuando la región \( R \) encerrada por las curvas \( y=x \) y \( y=x^{2} \) cuando: a) Se gira alrededor del eje \( x \). b) Se gira alrededor del eje \1 answer -
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In Exercises 15-36, find the transition points, intervals of increase/decrease, concavity, and asymptotic behavior. Then sketch the graph, with this information indicated. 15. \( y=x^{3}+24 x^{2} \) 12 answers -
(12 points) If \( x=y-\cos y \), find \( y^{\prime} \) and \( y^{\prime \prime} \) at the point where \( y=\pi / 4 \).2 answers