Calculus Archive: Questions from February 22, 2023
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7. Let \( x, y \), and \( z \) be the angles of a triangle. Determine the maximum value of \( f(x, y, z)=\sin x \sin y \sin z \).2 answers -
10. Find \( v^{*} \) if \( y=\frac{4}{3 x} \sin (3 r)+\frac{4}{3 \pi} \cos (5 r) \) 11. Find \( y^{\prime} \) if \( y=x e^{-x}+e^{\left(x^{2}\right)} \) 12 , Find \( \frac{d y}{d t} \), if \( y=(1+\co2 answers -
a. [6 Ptos] Hallar la integral que representa el volumen del sólido de revolución que se forma al rotar la región \( \Re_{3} \) con respecto al eje \( y=2 \). b. [6 Ptos] Hallar la integral que re2 answers -
11 Points] LARCALCET7 3.4.005. Complete the table. 11 Points] LARCALCET6 3.4.004. Complete the table.2 answers -
9. Write an equation of the tangent to each curve at the given point. a. \( y=2 x-\frac{1}{x}, P(0.5,-1) \) d. \( y=\frac{1}{x}\left(x^{2}+\frac{1}{x}\right), P(1,2) \) b. \( y=\frac{3}{x^{2}}-\frac{42 answers -
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Find all the second partial derivatives. \[ f(x, y)=x^{9} y^{8}+9 x^{6} y \] \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y)= \] \[ f_{y x}(x, y)= \] \[ f_{y y}(x, y)= \]2 answers -
Resolver las derivadas vectoriales
Descripción \[ \begin{array}{l} \mathbf{r}(t)=\left\langle t e^{-t}, 2 \arctan t, 2 e^{t}\right\rangle, \quad t=0 \\ \mathbf{r}(t)=\left\langle t^{3}+3 t, t^{2}+1,3 t+4\right\rangle, \quad t=1 \\ \ma2 answers -
1. Let \( f(x, y)=\ln \left(y^{2}+x^{3}\right) \). Compute \( D_{\left\langle\frac{1}{\sqrt{2}},-\frac{1}{\sqrt{2}}\right\rangle} f(-2,3) \).2 answers -
\( \frac{d y}{d x}: \) (a) \( y=\frac{16 \sqrt{x}+8 x^{3}-16}{x^{2}} \) (b) \( y=\sqrt{\frac{5}{x^{7}}-4 x^{3}} \).2 answers -
\( \frac{d y}{d x}: \) (a) \( y=\operatorname{Sin}\left(10 x^{4}+4 x\right) \) (b) \( y=\sin ^{3}\left(10 x^{4}+4 x\right) \).2 answers -
8. Find \( \frac{d y}{d x} \) : (a) \( y=\left(x^{5}\right) \cos \left(10 x^{4}\right) \) (b) \( y=\frac{x^{2}}{1+9 x^{2}} \).2 answers -
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If \( z(x, y)=f\left(x^{2}-y^{2}\right) \), then simplify \( y \frac{\partial z}{\partial x}+x \frac{\partial z}{\partial y} \).2 answers -
Section 13.7: Problem 8 (1 point) Calculate \( \iint_{\mathcal{S}} f(x, y, z) d S \) For \[ y=5-z^{2}, \quad 0 \leq x, z \leq 8 ; \quad f(x, y, z)=z \] \[ \iint_{\mathcal{S}} f(x, y, z) d S= \]2 answers -
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Descripción \[ \begin{array}{l} \mathbf{r}(t)=\left\langle t e^{-t}, 2 \arctan t, 2 e^{t}\right\rangle, \quad t=0 \\ \mathbf{r}(t)=\left\langle t^{3}+3 t, t^{2}+1,3 t+4\right\rangle, \quad t=1 \\ \ma2 answers -
Let \( f(x, y)=\ln \left(y^{2}+x^{3}\right) \). Compute \( D_{\left\langle\frac{1}{\sqrt{2}},-\frac{1}{\sqrt{2}}\right\rangle} f(-2,3) \).2 answers -
Find all the second partial derivatives. \[ \begin{array}{l} f(x, y)=x^{6} y-2 x^{5} y^{2} \\ f_{x x}(x, y)=6 x^{5} y-10 x^{4} y^{2} \\ f_{x y}(x, y)=4 x^{3}-20 x^{4} y \\ f_{y x}(x, y)=4 x^{3}-20 x^{2 answers -
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Find the first partial derivatives of the function. \[ \begin{array}{l} f(x, y, z, t)=4 x y z^{4} \tan (y t) \\ f_{x}(x, y, z, t)= \\ f_{y}(x, y, z, t)= \\ f_{z}(x, y, z, t)= \\ f_{t}(x, y, z, t)= \en2 answers -
#46 and 54
45-56 Use logarithmic differentiation to find the derivative of the function. 45. \( y=\left(x^{2}+2\right)^{2}\left(x^{4}+4\right)^{4} \) 46. \( y=\frac{e^{-x} \cos ^{2} x}{x^{2}+x+1} \) 47. \( y=\sq2 answers -
Find \( y^{\prime \prime} \) for the following function. \[ y=\csc x \sec x \] \[ \mathrm{y}^{\prime \prime}= \]2 answers -
Use implicit differentiation to find \( \frac{d r}{d \theta} \) \[ \tan \left(r \theta^{2}\right)=\frac{1}{3} \] \[ \frac{d r}{d \theta}= \]2 answers -
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Given , find
Given \( f(x, y)=5 x^{5}-6 x^{2} y^{3}+y^{6} \) \[ f_{x}(x, y)= \] \[ f_{y}(x, y)=[ \] \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y)= \]2 answers -
\( \begin{array}{l}\int(1+\cos 4 x)^{2} d x \\ \int \sec ^{9} 2 \theta \tan ^{3} 2 \theta d \theta\end{array} \)2 answers -
Pregunta 2 Sin responder aún Puntúa como \( 5.00 \) Calcular con dos decimales exactos \( \int_{1}^{3} \int_{2}^{3}(x+y)^{2} d y d x \) Respuesta: Respuesta2 answers -
Pregunta 1 Respuesta guardada Puntúa como \( 5.00 \) Sea \( \{(x, y): 2 \leq x \leq 3 ; 0 \leq y \leq x\} \) 1. La region no es tipo 2 . 2. La frontera de la region consiste en 4 segmentos y una curv2 answers -
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Una rosa de tres petalos esta dada por la curva \( r=\cos (3 \theta) \) 1. La convencion \( (-r, \theta)=(r, \theta+\pi) \) 2. El area de un petalo viene dado por \( \int_{-\pi / 3}^{\pi / 3} \int_{0}2 answers -
Find the exact length of the curve. x = 1/3 y (y − 3), 9 ≤ y ≤ 25
Find the exact length of the curve. \[ x=\frac{1}{3} \sqrt{y}(y-3), \quad 9 \leq y \leq 25 \]2 answers -
\[ f(x, y)=\sqrt[3]{x^{3}+y^{2}} \] a. El gradiente es el vector \( \left\langle\frac{3 x^{2}}{3\left(x^{3}+y^{2}\right)^{\frac{2}{3}}}, \frac{2 y}{3\left(x^{3}+y^{2}\right)^{\frac{2}{3}}}\right\rangl2 answers -
Find \( y^{\prime} \) by implicit differentiation. Match the expressions defining \( y \) implicitly with the letters labeling the expressions for \( y^{\prime} \). 1. \( 3 \cos (x-y)=6 y \sin x \) 2.2 answers -
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41 and 53
35-54. Continuity At what points of \( \mathbb{R}^{2} \) are the following functions continuous? 35. \( f(x, y)=x^{2}+2 x y-y^{3} \) 36. \( f(x, y)=\frac{x y}{x^{2} y^{2}+1} \) 37. \( p(x, y)=\frac{42 answers -
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Differentiate the function. \[ y=\left(7 x^{4}-x+4\right)\left(-x^{5}+7\right) \] \[ y^{\prime}= \] Differentiate the function. \[ y=\frac{3 x^{2}-8}{8 x^{3}+1} \]2 answers