Calculus Archive: Questions from July 29, 2022
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questions 228, 230, and 236 please
For the following exercises, find \( \frac{d y}{d x} \) for each function. \[ \text { 228. } y=\left(3 x^{2}+3 x-1\right)^{4} \] 229. \( y=(5-2 x)^{-2} \) 230. \( y=\cos ^{3}(\pi x) \) 231. \( y=\left1 answer -
In Problems 69-74, find \( f_{x x}(x, y), f_{x y}(x, y), f_{y x}(x, y) \), and \( f_{y y}(x, y) \) for each function \( f \). 2. \( f(x, y)=\frac{x^{2}}{y}-\frac{y^{2}}{x} \)3 answers -
\( \int\left(\frac{7 \sin (\sqrt{3 x+4})}{2 \sqrt{3 x+4}}\right) d x \) \( -\frac{14}{9} \cos \left(\frac{2}{9}(3 x+4)^{3 / 2}\right)+C \) \( -\frac{28}{3} \cos (\sqrt{3 x+4})+C \) \( -\frac{14}{3} \c1 answer -
Differentiate the function. \[ f(t)=\cos ^{2}\left(e^{\cos ^{2} t}\right) \] \[ f^{\prime}(t)=4 e^{\cos ^{2}(t)} \cos \left(e^{\cos ^{2}(t)}\right) \cos (t) \sin \left(e^{\cos ^{2}(t)}\right) \sin (t)1 answer -
1 answer
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\( y=\frac{2}{e^{x}} \) b) \( y=\pi^{x} \) \( f(x)=\cos \left(x^{2}-2 x\right)-\sin \left(\frac{4}{x^{2}}\right) \) d) \( y=3 \sin ^{2}(4 x) \)1 answer -
1 answer
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11. Guaranteed thumbs up, thank you!
Solve the equation explicitly for \( y \). \( y^{\prime \prime}+9 y=10 e^{2 t}, y(0)=-1, y^{\prime}(0)=1 \) \[ \begin{array}{l} y=-\frac{23}{13} \cos (3 t)-\frac{7}{39} \sin (3 t)+\frac{10}{13} e^{2 t1 answer -
1 answer
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(25 pts) In Problems 1-5, evaluate iterated integrals. 1. \( \int_{0}^{3} \int_{-2}^{0}\left(x^{2} y-2 x y\right) d y d x \) 2. \( \int_{1}^{4} \int_{0}^{4}\left(\frac{x}{2}+\sqrt{y}\right) d x d y \)3 answers -
1 answer
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Calculate div \( \mathbf{F} \) if \[ \begin{array}{l} \mathbf{F}(x, y, z)=\left\langle e^{x^{2}}+z, x^{2}+y^{2}+z^{2}, x^{2}-y z\right\rangle . \\ 2 x e^{z^{2}}+y \\ \left\langle 2 x e^{z^{2}}, 2 y,-y1 answer -
Find all the second partial derivatives. \[ f(x, y)=x^{7} y^{6}+5 x^{7} y \] \( f_{x x}(x, y)= \) \( f_{x y}(x, y)= \) \( f_{y x}(x, y)= \) \( f_{y y}(x, y)= \)1 answer -
Calculate \( \operatorname{curl} \mathbf{F} \) if \[ \mathbf{F}(x, y, z)=\left\langle x^{2}-x y, x y, y^{2}-x z\right\rangle \] \( \left\langle 2 y_{+}-z, x+y\right\rangle \) \[ (2 x-y, x,-x) \] \[ \l1 answer -
Find all the second partial derivatives. \[ f(x, y)=x^{4} y^{7}+8 x^{4} y \] \( f_{X X}(x, y)= \) \[ f_{x y}(x, y)= \] \( f_{y x}(x, y)= \) \[ f_{y y}(x, y)= \]3 answers -
Problem 3: Let \( f(x, y)=x y^{3}-5 x^{2}+3 x-x y+y^{4}+15 \) (a) Find \( f_{x}(x, y) \) and \( f_{y}(x, y) \). (b) Find \( f_{x x}(x, y), f_{x y}(x, y), f_{y x}(x, y) \) and \( f_{y y}(x, y) \).1 answer -
please help
Problem 3: Let \( f(x, y)=x y^{3}-5 x^{2}+3 x-x y+y^{4}+15 \) (a) Find \( f_{x}(x, y) \) and \( f_{y}(x, y) \). (b) Find \( f_{x x}(x, y), f_{x y}(x, y), f_{y x}(x, y) \) and \( f_{y y}(x, y) \).1 answer -
8.) Laplace Transforms using initial conditions \[ y^{\prime \prime}-y^{\prime}-2 y=0 \quad y(0)=1 y^{\prime}(0)=5 \]1 answer -
Find the gradient vector field \( \nabla f \) of \( f \). \[ f(x, y, z)=3 \sqrt{x^{2}+y^{2}+z^{2}} \] \( \nabla f(x, y, z)= \)1 answer -
Find the gradient vector field \( \nabla f \) of \( f \). \[ f(x, y)=7 \sqrt{x^{2}+y^{2}} \] \[ \nabla f(x, y)=\left\langle\frac{8 x}{\sqrt{x^{2}+y^{2}}}, \frac{8 y}{\sqrt{x^{2}+y^{2}}}\right\rangle \1 answer -
Find all the second partial derivatives. \[ f(x, y)=x^{5} y^{7}+4 x^{9} y \] \[ f_{X X}(x, y)= \] \[ f_{x y}(x, y)= \]1 answer -
Evaluate the Jacobian \( J(u, v, w) \) for the following transformation \[ \begin{array}{c} x=2 v w \\ y=2 u w \\ z=3 u^{2}-3 v^{2} \end{array} \] \( 8 w u^{2}-8 w v^{2} \) \( 24 w u^{2}-24 w v^{2} \)1 answer -
Please show work
Find the following for the function \( f(x, y)=3 x^{3} y^{2}-5 x+26 y-9 \). a. \( f(1,2)= \) b. \( f_{y}(x, y)= \) c. \( f_{x}(1,2)= \) d. \( f_{y y}(x, y)= \) e. \( f_{y x}(1,2)= \) f. \( f_{x x}(x,3 answers -
3 answers
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1 answer
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Please help! Will upvote
Given \( f(x, y)=-3 x^{4}+2 x^{2} y^{6}-4 y^{2} \) \( f_{x}(x, y)= \) \( f_{y}(x, y)= \) \( f_{x x}(x, y)= \) \( f_{x y}(x, y)= \)1 answer -
Find the first partial derivatives of the functions A) B)
\( f(x, y)=\frac{4(x-y)}{x+y} \) \( f_{x}(x, y)= \) \( f_{y}(x, y)= \) Find the first partial derivatives of the function. \[ f(x, y, z)=x z-9 x^{9} y^{3} z^{9} \] \( f_{X}(x, y, z)= \) \( f_{y}(x, y1 answer -
Find the first partial derivatives of the following functions. a) B)
\( f(x, y, z)=\frac{7 x}{y+z} \) \( f_{x}(x, y, z)= \) \( f_{y}(x, y, z)= \) \( f_{z}(x, y, z)= \) \( f(x, y, z, t)=x y^{2} z^{4} t^{6} \) \( f_{x}(x, y, z, t)= \) \( f_{y}(x, y, z, t)= \) \( f_{z}(x1 answer -
pls help...will upvote
Given \( f(x, y)=-4 x^{5}-2 x y^{2}+3 y^{3} \) \[ \begin{array}{l} f_{x}(x, y)= \\ f_{y}(x, y)= \end{array} \] Given \( f(x, y)=-2 x^{5}+4 x y^{3}+y^{4} \), find the following numerical values: \[ \b1 answer -
pls help...will upvote
Given \( z=f(x, y)=-3 e^{2 x}+x y^{3}-5 y^{5}-6 \ln (y) \) \[ z_{x}(x, y)= \] \[ z_{y}(x, y)= \] Given \( f(x, y)=5 x^{4}+6 x y^{2}+y^{5} \), find the following numerical values: \[ \begin{array}{l}1 answer -
Find all the second partial derivatives. \[ \begin{array}{c} f(x, y)=x^{6} y^{7}+4 x^{7} y \\ f_{X x}(x, y)=30 y^{7} x^{4}+168 x^{5} y \\ f_{x y}(x, y)=30 y^{7} x^{4}+168 x^{5} y \\ f_{y x}(x, y)= \\1 answer -
Solve the initial value problem. \[ \frac{1}{\theta} \frac{d y}{d \theta}=\frac{y \cos \theta}{y^{4}+1}, y\left(\frac{\pi}{2}\right)=1 \]2 answers -
will you plz answer these few questions... i will upvote.
Given \( f(x, y)=3 x^{2}-4 x^{2} y^{6}+5 y^{5} \), find \[ f_{x}(x, y)= \] \( f_{y}(x, y)= \) \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y)= \] \[ f_{y y}(x, y)= \] \[ f_{y x}\left(x, \frac{1}{y}\right)= \] Q1 answer -
Given \( f(x, y)=-x^{4}+x^{2} y^{6}-5 y^{5} \) \( f_{x}(x, y)= \) \( f_{y}(x, y)= \) \( f_{x x}(x, y)= \) \( f_{x y}(x, y)= \)1 answer