Calculus Archive: Questions from February 04, 2023
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\( \int_{-3}^{3} \int_{-\sqrt{9-x^{2}}}^{\sqrt{9-x^{2}}} \int_{0}^{\sqrt{9-x^{2}-y^{2}}} z \sqrt{x^{2}+y^{2}+z^{2}} d z d y d x \).2 answers -
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Determine el área del paralelogramo que tiene los vectores \( \vec{v}=i-2 j+6 k y \vec{w}=-5 j+2 k \) como lados adyacentes. \( \sqrt{123} \) \( \sqrt{219} \) \( 3 \sqrt{195} \) \( \sqrt{705} \) Ning2 answers -
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Please explain the answer.
Complete the table. \[ \begin{array}{l|l|l} \boldsymbol{y}=\boldsymbol{f}(\boldsymbol{g}(\boldsymbol{x})) & \boldsymbol{u}=\boldsymbol{g}(\boldsymbol{x}) & \boldsymbol{y}=\boldsymbol{f}(\boldsymbol{u}2 answers -
Calculate the integral (a) \( \int_{-\infty}^{\infty} x^{5} e^{-x^{2}} d x \) (b) \( \int_{\pi / 4}^{\pi / 3} \frac{\sqrt{\tan \theta}}{\sin 2 \theta} d \theta \) (c) \( \int \frac{x^{2}+1}{x^{4}+x^{22 answers -
Find \( \frac{\partial f}{\partial x} \) and \( \frac{\partial f}{\partial y} \) \[ f(x, y)=(3 x-3 y)^{3} \] b. \( f(x, y)=e^{-x} \sin (2 x+y) \)2 answers -
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Hallar un vector unitario y ortogonal a los vectores \( \vec{A}=i-4 j+k, \vec{B}=2 i+3 j \) \[ \begin{array}{l} -\frac{\sqrt{3}}{\sqrt{134}} i+\frac{2}{\sqrt{134}} j+\frac{11}{\sqrt{134}} k \\ -\frac{2 answers -
Differentiate \[ \begin{array}{l} h(w)=\left(w^{5}+4 w^{4}\right)\left(w^{-4}-w^{-6}\right) \\ h(w)= \\ y=\frac{e^{x}}{7-e^{x}} \\ y^{\prime}= \\ f(x)=\frac{1}{2 x^{3}-5 x^{2}+9} \\ f^{\prime}(x)= \\2 answers -
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escriba el número indicado en la forma a+ib
9. \( (2-3 i)(4+i) \) 12. \( (1-i)^{3} \) 17. \( \frac{(3-i)(2+3 i)}{1+i} \)2 answers -
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encuentre z1z2 y z1/z2. Escriba el número en la forma a+ib.
5. \( z_{1}=2\left(\cos \frac{\pi}{8}+i \operatorname{sen} \frac{\pi}{8}\right), z_{2}=4\left(\cos \frac{3 \pi}{8}+i \operatorname{sen} \frac{3 \pi}{8}\right) \)2 answers -
1. Clasificar si los siguientes pares de vectores son paralelos, perpendiculareso ninguno de los dos. a. \( \vec{A}=i+2 j-k \quad \vec{B}=2 i+2 j+6 k \) b. \( \vec{C}=i+2 j-k \quad \vec{D}=3 i+6 j-3 k2 answers -
(1 point) Solve the initial-value problem \( x y^{\prime}=y+x^{2} \sin x, y\left(\frac{\pi}{4}\right)=0 \) Answer: \( y(x) \)2 answers -
1) Resuelva las siguientes operaciones de vectores ( 10 ptos) a) Halle \( |\bar{a}|,|\bar{b}|, 3 \bar{a}+5 \bar{b} \) si \( \bar{a}=\langle 3,-4,-1\rangle, \bar{b}=\langle-2,5,4\rangle \) b) Sean \( \2 answers -
For the function, find the partials \( f_{x}(x, y) \) and \( f_{y}(x, y) \). \[ f(x, y)=\left(3 x^{2}+7 x y+5\right)^{4} \] (a) \( f_{x}(x, y) \) (b) \( f_{y}(x, y) \)2 answers -
For the function, find the partials \( f_{x}(x, y) \) and \( f_{y}(x, y) \). \[ f(x, y)=\left(4 x^{2}+3 x y+4\right)^{4} \] (a) \( f_{x}(x, y) \) (b) \( f_{y}(x, y) \)2 answers -
a) Encuentre la derivada y el vector tangente \( \bar{T}(t) \) en \( t=0 \) para la función \( \bar{r}(t)=\langle\cos t, 3 t, 2 \operatorname{sen} 2 t\rangle \) b) Determine el vector gradiente \( \n2 answers -
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