Calculus Archive: Questions from March 19, 2023
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4. Find the derivative of each function. (a) \( y=10 e^{x} \) (b) \( y=e^{x^{2}-3 x+7} \) (c) \( y=(x+2)^{3} e^{-5 x} \) (d) \( y=\frac{x^{2} e^{2 x}}{x+e^{3 x}} \) (e) \( y=3 \cdot 7^{\sqrt{x}} \)2 answers -
6. Find the derivative of each function. (a) \( y=15 \ln x \) (b) \( y=x^{4} \ln \left(x^{3}+e^{-x}\right) \) (c) \( y=\frac{e^{5 x}}{\ln (3 x)} \) (d) \( y=\log _{7} \sqrt{4 x-3} \) (e) \( y=(1+\ln |2 answers -
2 answers
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2 answers
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Solve the initial value problems. \[ y^{\prime \prime}-2 y^{\prime}-15 y=0, \quad y(0)=-1, y^{\prime}(0)=2 . \] Answer: \( y=-\frac{1}{8} e^{5 x}-\frac{7}{8} e^{-3 x} \)2 answers -
\( \begin{array}{l}\text { If } z=\cos ^{-1} \frac{y}{\sqrt{x^{2}+y^{2}}} \text {, determine } \\ 2.2 .1 \frac{\partial z}{\partial y} . \\ 2.2 .2 \frac{\partial^{2} z}{y^{2}} .\end{array} \)2 answers -
Find the derivative of the function. \[ \begin{aligned} y= & \frac{1}{6}(8 x+11)^{3}+\left(1-\frac{1}{x^{3}}\right)^{-1} \\ & 4(8 x+11)^{2}-\frac{3}{x^{4}}\left(1-\frac{1}{x^{3}}\right)^{-2} \\ & \fra2 answers -
2 answers
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Fill in the blanks: 1. If \( \tan x=1 \) then \( \tan (-x)= \) 2. If \( \sin x=0.2 \) then \( \sin (-x)= \) 3. If \( \cos x=0.3 \) then \( \cos (-x)= \) 4. If \( \tan x=-1.5 \) then \( \tan (\pi+x)= \2 answers -
2 answers
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Q1
Hallar el diferencial total de \( f(x, y, z)=e^{y} \cos (2 x)+z^{2} \) en el punto \( P(1,1,0) \)2 answers -
2 answers
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please solve only "b". thx
Solve the following differential equation. (a) \( y^{\prime \prime}+3 y^{\prime}-4 y=0 \) (b) \( y^{\prime \prime}+4 y^{\prime}+13 y=0 \) (c) \( y^{\prime \prime}+6 y^{\prime}+9 y=0 \) (d) \( y^{\prim2 answers -
Find the first partial derivatives with respect to \( x, y \), and \( z \). \[ f(x, y, z)=3 x^{2} y-4 x y z+6 y z^{2} \] \[ f_{x}(x, y, z)= \] \[ f_{y}(x, y, z)= \] \[ f_{z}(x, y, z)= \]2 answers -
PARTE 1 (Dol 15 al 22 de fabrero] Usted y su equipo de trabajo han sido contratados para diaenar un matra2. Un miembeo de sa equipo ha tenido la siguiente idea. 1. Lo primero que han hecho es el caso0 answers -
\( \begin{array}{l}\text { Calculate } \frac{d^{2} y}{d x^{2}} \\ \qquad y=e^{-(x-2)}-x \\ \frac{d^{2} y}{d x^{2}}=\end{array} \)2 answers -
\( \begin{array}{l}\text { Calculate } \frac{d^{2} y}{d x^{2}} . \\ \qquad y=0.3 x-0.3 \\ \frac{d^{2} y}{d x^{2}}=\end{array} \)2 answers -
7. Find each limit for the function \( f(x, y)=x \sqrt{y} \) a) \( \lim _{\Delta x \rightarrow 0} \frac{f(x+\Delta x, y)-f(x, y)}{\Delta x} \) b) \( \lim _{\Delta y \rightarrow 0} \frac{f(x, y+\Delta2 answers -
a, b y c
II. Determine e interprete la curvatura \( \mathrm{K} \) de la curva en el valor del parámetro dado a) \( r(t)=t^{2} i+j ; t=2 \) b) \( r(t)=\left(3 t, 2 t^{2}\right) \) en el punto \( (-3,2) \) c) \2 answers -
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2 answers
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please just solve for "d". thx
34. Solve the following differential equation. (a) \( y^{\prime \prime}+3 y^{\prime}-4 y=0 \) (b) \( y^{\prime \prime}+4 y^{\prime}+13 y=0 \) (c) \( y^{\prime \prime}+6 y^{\prime}+9 y=0 \) (d) \( y^{\2 answers -
2 answers
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Show all work please.
1. Differentiate. (a) \( y=\ln \left(3 x^{2}\right) \) (b) \( y=2 x e^{3 x} \) (c) \( y=\frac{\ln x}{x^{2}} \)2 answers -
What does \( \int_{0}^{1 / 2} \frac{\sqrt{x}}{\sqrt{1-x}} d x \) become if you use the substituion \( \sqrt{x}=\sin y \) ?2 answers -
I. Determine the length of the arc in the given interval. II. Determine and interpret the curvature K of the curve at the given parameter value.
I. Determine la longitud del arco en el intervalo dado a) \( r(t)=i+t^{2} j+t^{3} k ;[0,2] \) b) \( r(t)=\langle 4 t,-\cos t, \operatorname{sen} t) ;\left[0, \frac{3 \pi}{2}\right] \) II. Determine e2 answers -
Hallar el diferencial total de \( f(x, y, z)=e^{y} \cos (2 x)+z^{2} \) en el punto \( P(1,1,0) \) Attach File Find the total differential of \( f(x, y, z)=e^{\prime} \cos (2 x)+z 2 \) at the point \(2 answers -
Dada \( f(x, y, z)=\frac{3 x z}{x+y} \). Hallar \( f_{x}(1,1,0), f_{y}(1,0,1) \) y \( f_{z}(0,1,1) \).2 answers -
Find \( y^{\prime} \) and \( y^{\prime \prime} \) for \( x^{2}+4 x y-7 y^{2}=8 \). \[ y^{\prime}= \] \[ y^{\prime \prime}= \]2 answers -
2 answers
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2 answers
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2 answers
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Hallar el diferencial total de \( g(x, y, z)=x^{2} y z^{2}+\sin (y z) \) en el punto \( P(0,1,1) \).2 answers -
2 answers
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Directions: List all possible rational zeros. Then find the actual zeros 7. f(x)=x^(3)+2x^(2)-11x-122 answers
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find the curl for these 3
3 Find the curl: \[ \mathbf{F}(x, y, z)=\sin (y z) \mathbf{i}+\sin (z x) \mathbf{j}+\sin (x y) \mathbf{k} \] Makin S'mores \[ \begin{array}{c} \langle x \cos (x y)-x \cos (z x), y \cos (y z)-y \cos (x2 answers -
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pls help find the derivative for #19 not sure if i use product or quotient ruke
3-30 Differentiate. 3. \( y=\left(4 x^{2}+3\right)(2 x+5) \) 4. \( y=\left(10 x^{2}+7 x-2\right)\left(2-x^{2}\right) \) 5. \( y=x^{3} e^{x} \) 6. \( y=\left(e^{x}+2\right)\left(2 e^{x}-1\right) \) 7.2 answers -
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4. (10 puntos) Usa una sustitución para convertir la integral a una integral de funciones racionales. Luego usa fracciones parciales para encontrar la integral. b. \( \int \frac{e^{x} d x}{\left(e^{2 answers -
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(1 point) Find the solution of \[ y^{\prime \prime}-2 y^{\prime}+y=18 e^{4 t} \] with \( y(0)=3 \) and \( y^{\prime}(0)=3 \). ( 1 point) Find a particular solution to \[ y^{\prime \prime}+5 y^{\prime2 answers