Calculus Archive: Questions from August 04, 2023
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Find \( \operatorname{div} \mathbf{F} \) and curl \( \mathbf{F} \) if \( \mathbf{F}(x, y, z)=9 y^{7} z^{6} \mathbf{i}-12 x^{7} z^{9} \mathbf{j}-4 x y^{5} \mathbf{k} \). \( \operatorname{div} \mathbf{F2 answers -
Find \( \nabla \cdot(\nabla \times \mathbf{F}) \) if \( \mathbf{F}(x, y, z)=4 \sin x \mathbf{i}+3 \cos (4 x-5 y) \mathbf{j}+10 z \mathbf{k} \) \[ \nabla \cdot(\nabla \times \mathbf{F})=[\quad] \]2 answers -
Find \( \nabla \cdot(\nabla \times \mathbf{F}) \), if \( \mathbf{F}(x, y, z)=2 e^{x z} \mathbf{i}+6 x e^{y} \mathbf{j}-4 e^{y z} \mathbf{k} \) \[ \nabla \cdot(\nabla \times \mathbf{F})= \]2 answers -
Find the gradient vector field \( \nabla f \) of \( f \). \[ f(x, y, z)=x^{3} y e^{y / z} \] \[ \nabla f(x, y, z)= \]2 answers -
Given \( y=x^{3}-27 x+17 \) a) Find \( y^{\prime}= \) b) Find \( y^{\prime \prime}= \) Critical values of \( y^{\prime} \) at \( x= \) No Critical values of \( y^{\prime} \) Critical values of \( y^{\2 answers -
K Find d²y 2 dx 7x+9y = 8 sin (y) d²y 2 dx 11 0 ...
Find \( \frac{d^{2} y}{d x^{2}} \) \[ 7 x+9 y=8 \sin (y) \] \[ \frac{d^{2} y}{d x^{2}}= \]2 answers -
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Given \( y=4 x^{3}-300 x+11 \) a) Find \( y^{\prime}= \) b) Find \( y^{\prime \prime}= \) Critical values of \( y^{\prime} \) at \( x= \) No Critical values of \( y^{\prime} \) Critical values of \( y2 answers -
Find \( \iint_{D}(2 x+y) d A \) where \( D=\left\{(x, y) \mid x^{2}+y^{2} \leq 25, x \geq 0\right\} \) Find \( \iint_{D} \cos \left(x^{2}+y^{2}\right) d A \) where \( D=\left\{(x, y) \mid 9 \leq x^2 answers -
valuate \( \iiint_{E} 3 x z d V \) where \( E=\{(x, y, z) \mid 0 \leq x \leq 1, x \leq y \leq 2 x, 0 \leq z \leq x+2 y\} \) Find the volume of the solid bounded by the paraboloids \( z=-4+2 x^{2}+22 answers -
Part 1 of 2 Let \( \vec{F}(x, y, z)=z^{2} \hat{\imath}+2 y \hat{\jmath}+2 x z \hat{k} \). Consider the line integral \[ \int_{C} \vec{F}(x, y, z) \cdot d \vec{r} \] Let \( f(x, y, z)=x z^{2}+y^{2}+3 \2 answers -
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y" - 4y' + 4y = te², y(0) = 1, y '(0) = 7 find y(s)
\( y^{\prime \prime}-4 y^{\prime}+4 y=t e^{2 t}, y(0)=1, y^{\prime}(0)=7 \)2 answers -
y"– 4y' + 4y = te², y(0) = 1, y'(0) = 7 solve using laplace transform
\( y^{\prime \prime}-4 y^{\prime}+4 y=t e^{2 t}, y(0)=1, y^{\prime}(0)=7 \)2 answers -
If \( y=\left(x^{2}-\sin x\right)^{4} \) then \( y^{\prime}= \) \[ \begin{array}{l} 4\left(x^{2}-\sin x\right)^{3} \cdot(2 x-\cos x) \\ 4(2 x-\cos x)^{3} \cdot\left(x^{2}-\sin x\right) \\ 4(2 x-\cos x2 answers -
Calculate \( \iint_{\mathcal{S}} f(x, y, z) d S \) For \[ y=9-z^{2}, \quad 0 \leq x, z \leq 9 ; \quad f(x, y, z)=z \] \[ \iint_{\mathcal{S}} f(x, y, z) d S= \]2 answers -
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Find the first partial derivatives of the function. f(x, y) = 4(x − y)/ x + y fx(x, y)= fy(x, y) =2 answers
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Find the derivative of \( y=\ln \left(\frac{\left(x^{2}-12 x\right)^{3}}{\sqrt{x^{3}-9}}\right) \) \[ y^{\prime}=\frac{2 x-12}{x^{2}-12 x}-\frac{3 x^{2}}{x^{3}+9} \] \[ y^{\prime}=\frac{6 x-24}{x^{2}-2 answers -
Find the derivative of \( y=e^{\sqrt{x^{2}+3}} \) \[ \begin{array}{l} y^{\prime}=2 x e^{\sqrt{x^{2}+3}} \\ y^{\prime}=\frac{\sqrt{2 x}}{x^{2}+3} \\ y^{\prime}=\frac{e^{\sqrt{x^{2}+3}}}{\sqrt{x^{2}+3}}2 answers -
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Find \( \iint_{D} \cos \left(x^{2}+y^{2}\right) d A \) where \( D=\left\{(x, y) \mid 9 \leq x^{2}+y^{2} \leq 25\right\} \)2 answers -
Given \( y=x^{3}-75 x+15 \) a) Find \( y^{\prime}= \) b) Find \( y^{\prime \prime}= \) Critical values of \( y^{\prime} \) at \( x= \) No Critical values of \( y^{\prime} \) Critical values of \( y^{\2 answers -
Find \( y^{\prime \prime} \). \[ y=\left(x^{9}+x\right)^{5 / 6} \] Choose the correct expression for \( y^{\prime \prime} \) below. A. \( \frac{5}{6}\left(x^{9}+x\right)^{-1 / 6}\left(9 x^{8}+1\right)2 answers -
Determine the following indefinite integral. \[ \int \frac{-6+5 \cos y}{\sin ^{2} y} d y \] \[ \int \frac{-6+5 \cos y}{\sin ^{2} y} d y= \]2 answers -
Let \( h(x, y, z)=x y e^{z}+\frac{x}{y} \). Compute \( h(8,1,0), h(-8,1,1) \), and \( h(8,-1,1) \). \[ h(8,1,0) \text {, = } \] \[ h(-8,1,1),= \] \[ h(8,-1,1),= \]2 answers -
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