Calculus Archive: Questions from December 03, 2023
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7- The result of \( \left(D_{1}+D_{1}\right)\left(e^{*-1} x y^{2}\right)= \) a) \( e^{x-1}\left(y^{\prime}+2 x y\right) \) b) \( e^{x-y}\left(y^{2}+2 y\right) \) c) \( e^{(n)}\left(x^{2}+2 x y\right)1 answer -
15. The general solution of \( p \cot x+q \cot y=\cot z \) is a) \( \psi\left(\frac{\cos x}{\cos y}, \frac{\sin y}{\sin z}\right)=0 \) b) \( v\left(\frac{\sin x}{\sin y}, \frac{\cos y}{\cos z}\right)=1 answer -
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8[ k=1 (k!) (3k) (2k)! classify the convergence
\( \sum_{k=1}^{\infty} \frac{(k !)\left(3^{k}\right)}{(2 k) !} \)1 answer -
2. Establecer, pero no evaluar, una integral triple para el volumen de la pirámide encerrada por los planos \[ \frac{x}{B}+\frac{y}{C}+\frac{z}{D}=1, \quad x=0, \quad y=0, \quad z=0 \] Nota: Los vér1 answer -
3. Calcular el campo gradiente de la función \[ \begin{array}{c} f(x, y, z)=\frac{A x}{C y+E z} \\ f(x, y, z)=\frac{2 x}{6 y+5 x} \end{array} \]1 answer -
4. Calcular la divergencia de este campo vectorial. \[ \begin{array}{l} \overrightarrow{\mathbf{F}}(x, y, z)=\left(\frac{B x}{x^{2}+y^{2}+z^{2}}\right) \hat{\mathbf{i}}+\left(\frac{D y}{x^{2}+y^{2}+z^1 answer -
5. Calcular el curl de este campo vectorial. \[ \begin{array}{l} \overrightarrow{\mathbf{F}}(x, y, z)=(A x+B y+C z) \hat{\mathbf{i}}+(B x+C y+D z) \hat{\mathbf{j}}+(C x+D y+E z) \hat{\mathbf{k}} \\ \o1 answer -
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In Exercises 1-27, sketch the graph of the function. 1. \( y=x^{2}-5 x+4 \) 2. \( y=4-x^{2} \) 3. \( y=x^{3}-3 x+3 \) 4. \( y=-2 x^{3}+6 x^{2}-3 \) 5. \( y=1-9 x-6 x^{2}-x^{3} \) 6. \( y=(x-2)^{3}+1 \1 answer -
(1 point) Let \( F(x, y, z)=\left(8 x z^{2}, 8 x y z, x y^{3} z\right) \) be a vector field and \( f(x, y, z)=x^{3} y^{2} z \). \[ \begin{array}{l} \nabla f=( \\ \nabla \times F=( \\ F \times \nabla f1 answer -
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I need f sub xy(x,y)
Given \( f(x, y)=5 x^{5}+6 x y^{3}-5 y^{2} \) \[ \begin{array}{l} f_{x x}(x, y)= \\ f_{x y}(x, y)= \end{array} \]1 answer -
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o. \( \int \sin ^{3}(2 x) \cos (2 x) d x \) d. \( \int_{0}^{\frac{\pi}{3}} \frac{\sin (x)}{\cos ^{2}(x)} d x \)1 answer -
Evaluate the triple integral. \[ \iiint_{E} 6 x d V \text {, where } E=\left\{(x, y, z) \mid 0 \leq y \leq 2,0 \leq x \leq \sqrt{4-y^{2}}, 0 \leq z \leq 2 y\right\} \]1 answer -
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Question 18, thank you!
13-28 Sketch the region enclosed by the given curves and find its area. 13. \( y=12-x^{2}, \quad y=x^{2}-6 \) 14. \( y=x^{2}, \quad y=4 x-x^{2} \) 15. \( y=\sec ^{2} x, \quad y=8 \cos x, \quad-\pi / 31 answer -
(a) \( y^{\prime \prime}+3 y^{\prime}+2 y=30 e^{2 x}, y(0)=1, y^{\prime}(0)=0 \) (b) \( y^{\prime \prime}-y^{\prime}-12 y=144 x^{3}+25 / 2, y(0)=5, y^{\prime}(0)=-1 / 2 \) (c) \( y^{\prime \prime}+4 y1 answer -
(a) \( y^{\prime \prime}-2 y^{\prime}-3 y=0, y(0)=2, y^{\prime}(0)=14 \) (b) \( y^{\prime \prime}+2 y^{\prime}+y=0, y(0)=4, y^{\prime}(0)=-6 \) (c) \( 10 y^{\prime \prime}-50 y^{\prime}+65 y=0, y(0)=31 answer -
r = 8; (h, k) = (1, -9) O(x-1)²+ (x - 1)² + (y + 9)² = 64 O(x - 1)² + (y + 9)² = 1 O(x + 1)² + (y- 9)² = 64 kay /x + 1)² + (y - 9)² = 8
\( \begin{array}{c}r=8 ;(h, k)=(1,-9) \\ (x-1)^{2}+(y+9)^{2}=64 \\ (x-1)^{2}+(y+9)^{2}=8 \\ (x+1)^{2}+(y-9)^{2}=64 \\ (x+1)^{2}+(y-9)^{2}=8\end{array} \)1 answer -
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Let f (x, y) = sin(x3)y + cos(y3)x. Find fxxyy(x, y)
\( f(x, y)=\sin \left(x^{3}\right) y+\cos \left(y^{3}\right) x \). Find \( f_{x x y y}(x, y) \)1 answer -
Let f (x, y) = sin(x3)y + cos(y3)x. Find fxxyy(x, y)
\( f(x, y)=\sin \left(x^{3}\right) y+\cos \left(y^{3}\right) x \). Find \( f_{x x y y}(x, y) \)1 answer -
15.6/2
\[ \int_{0}^{1} \int_{0}^{2 \pi} \int_{0}^{\pi} y \sin z d x d y d z \] \[ \int_{0}^{1} \int_{0}^{2 \pi} \int_{0}^{\pi} y \sin z d x d y d z= \] (Type an exact answer.)1 answer -
#24
21-24 Evaluate the line integral \( \int_{C} \mathbf{F} \cdot d \mathbf{r} \), where \( C \) is given by the vector function \( \mathbf{r}(t) \). 21. \[ \begin{array}{l} \mathbf{F}(x, y)=x y^{2} \math1 answer -
find y
\( y=\frac{\sin \theta+\cos \theta}{\sin \theta-\cos \theta} \) \( y=\frac{\sin \theta+\cos \theta}{\sin \theta-\cos \theta} \)1 answer -
Differentiate the function y= 10/ln(x) y'=
Differentiate the function. \[ y=\frac{10}{\ln x} \] \[ y^{\prime}= \]1 answer -
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√3 5-¹1(-13³) 2 b) cos tan-¹(-3) c) tan Need Help? Read It
\( \cos ^{-1}\left(-\frac{\sqrt{3}}{2}\right) \) \( \tan ^{-1}\left(-\frac{\sqrt{3}}{3}\right) \)1 answer -
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\( \begin{array}{l}\text { ve } y^{\prime}=\frac{y^{2}}{x^{2}}, y(1)=\frac{1}{2} \\ y=\frac{1}{x+1} \\ y=\left(x^{3}+1\right)^{1 / 3} \\ y=\frac{x}{x+1} \\ y=\left(x^{3}+\frac{7}{8}\right)^{1 / 3}\end1 answer -
For the given position vectors \( \mathbf{r}(t) \), compute the (tangent) velocity vector \( \mathbf{r}^{\prime}(t) \) for the given value of \( t \). A) Let \( \mathbf{r}(t)=(\cos 5 t, \sin 5 t) \).1 answer -
Draw the region and find its area. Explain your results.
Dibuje la región y encuentre su área: \[ S=\left\{(x, y) / x \leq 1,0 \leq y \leq e^{x}\right\} \]1 answer -
3. [ 25 points] Solve the following: (a) \( y^{\prime \prime}+3 y^{\prime}+2 y=30 e^{2 x}, y(0)=1, y^{\prime}(0)=0 \) (b) \( y^{\prime \prime}-y^{\prime}-12 y=144 x^{3}+25 / 2, y(0)=5, y^{\prime}(0)=-1 answer -
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Given f(x,y)=4x^(5)y-7xy^(2). Compute: {:[(del^(2)f)/(delx^(2))=],[(del^(2)f)/(dely^(2))=]:}
Given \( f(x, y)=4 x^{5} y-7 x y^{2} \). Compute: \[ \begin{array}{l} \frac{\partial^{2} f}{\partial x^{2}}= \\ \frac{\partial^{2} f}{\partial y^{2}}= \end{array} \]1 answer -
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Calculate \( \iint_{\mathcal{S}} f(x, y, z) d S \) For \[ x^{2}+y^{2}=9, \quad 0 \leq z \leq 5 ; \quad f(x, y, z)=e^{-z} \] \[ \iint_{\mathcal{S}} f(x, y, z) d S= \]1 answer -
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Differentiate the function. y= csc^6 (10x)
\( \begin{array}{l}y^{\prime}=60 \csc ^{5}(10 x) \\ y^{\prime}=-6 \csc ^{6}(10 x) \cot (10 x) \\ y^{\prime}=-10 \csc ^{6}(10 x) \cot (10 x) \\ y^{\prime}=-60 \csc ^{6}(10 x) \cot (10 x) \\ y^{\prime}=1 answer -
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In Problems 25-32, find the indicated value. 26. \( f_{x}(4,1) \) if \( f(x, y)=x^{2} y^{2}-5 x y^{3} \) 28. \( f_{y}(2,4) \) if \( f(x, y)=x^{4} \ln y \)1 answer -
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Solve. \[ \frac{d y}{d x}=\frac{9}{y} \] A. \( y=18 x+C \) B. \( y=\sqrt{18 x+C} \), or \( y=-\sqrt{18 x+C} \) C. \( y=\sqrt{18 x+C} \) D. \( y=\sqrt{9 x+C} \), or \( y=-\sqrt{9 x+C} \)1 answer -
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Determine el área total de las regiones sombreadas de la siguiente gráfica. Exprese su resultado en decimal1 answer -
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0. If \( \int_{1}^{5} f(x) d x=12 \) and \( \int_{4}^{5} f(x) d x=3.6 \), find \( \int_{1}^{4} f(x) d x \).1 answer -
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#42
In Problems 25-32, find the indicated value. 26. \( f_{x}(4,1) \) if \( f(x, y)=x^{2} y^{2}-5 x y^{3} \) 28. \( f_{y}(2,4) \) if \( f(x, y)=x^{4} \ln y \) 42. \( f_{y y}(x, y) \) if \( f(x, y)=x^{2}+90 answers