Calculus Archive: Questions from August 05, 2023
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Let \( y \) be the solution of IVP \( y^{\prime \prime \prime}+3 y^{\prime \prime}+3 y^{\prime}+y=0, y(0)=1, y^{\prime}(0)=0, y^{\prime \prime}(0)=1 \). Then \( y(-1)= \) a. \( -e \) b.e c. \( 2 e \)2 answers -
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solve 27, 29, 31, 34
27-34 Calculate the double integral. 27. \( \iint_{R} x \sec ^{2} y d A, \quad R=\{(x, y) \mid 0 \leqslant x \leqslant 2,0 \leqslant y \leqslant \pi / 4\} \) 28. \( \iint_{R}\left(y+x y^{-2}\right) d2 answers -
\( x=-(8 u+7 u v), y=-(2 u v+4 u v w) \), and \( z=-10 u v w \) implies \( \frac{\partial(x, y, z)}{\partial(u, v, w)}= \)2 answers -
15, 17, 19, 21, 23, 25, 27, 29, 31 with steps please!
15-48. Derivatives Find the derivative of the following finctions. 15. \( y=\ln 7 x \) 16. \( y=x^{2} \ln x \) 17. \( y=\ln x^{2} \) 18. \( y=\ln 2 x^{8} \) 19. \( y=\ln |\sin x| \) 20. \( y=\frac{1+\2 answers -
23, 25, 27, 29, 31, 33, 35, 37, 37 with steps please
23. \( y=\ln \left(\frac{x+1}{x-1}\right) \) 25. \( y=\left(x^{2}+1\right) \ln x \) 27. \( y=x^{2}\left(1-\ln x^{2}\right) \) 29. \( y=\ln (\ln x) \) 31. \( y=\frac{\ln x}{\ln x+1} \) 33. \( y=x^{e} \2 answers -
\( x=7 u-5 v-7 w, y=7 v-u-w \), and \( z=8 v-8 u+w \) implies \( \frac{\partial(x, y, z)}{\partial(u, v, w)}= \)2 answers -
Quiero el desarrollo bien detallado paso a paso del problema, es del tema de Conducciones cerradas con bombas. Lo necesito para hoy por favor. El ejercicio 3 se va resolver con los datos obtenidos de
Ejercicio 3 (Conducciones cerradas con bombas): 2 puntos Dando por buenos los resultados obtenidos en el ejercicio anterior, determina: 1. La presión que estaría existiendo a la entrada de la bomba.2 answers -
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No need to show work
Question 34 Let \( g(x, y)=(5 x+2 y)^{10} \). Find \( g_{x}(x, y) \). \[ \begin{array}{l} g_{x}(x, y)=10(5 x+2 y)^{9} \\ g_{x}(x, y)=1024 \\ g_{x}(x, y)=50(5 x+2 y)^{9} \\ g_{x}(x, y)=20 y^{9} \end{ar2 answers -
Find the first partial derivatives of the function. \[ f(x, y, z)=7 x \sqrt{y z} \] \[ f_{x}(x, y, z)= \] \[ f_{y}(x, y, z)= \] \[ r_{z}(x, y, z)= \]2 answers -
\( x=u+8 v-3 w, y=10 v-9 u-10 w \), and \( z=5 u+v+3 w \) implies \( \frac{\partial(x, y, z)}{\partial(u, v, w)}= \)2 answers -
\( x=u v-10 u, y=3 u v+u v w \), and \( z=-6 u v w \) implies \( \frac{\partial(x, y, z)}{\partial(u, v, w)}= \)2 answers -
Find the Jacobian of the transformation. \[ x=8 v+8 w^{2}, \quad y=9 w+9 u^{2}, \quad z=7 u+7 v^{2} \] \[ \frac{\partial(x, y, z)}{\partial(u, v, w)}= \]2 answers -
Find the gradient vector field of \( f \). \[ f(x, y, z)=6 \sqrt{x^{2}+y^{2}+z^{2}} \] \[ \nabla f(x, y, z)= \]4 answers -
Find the gradient vector field \( \mathrm{V} f \) of \( t \) and sketch it. \[ f(x, y)=7 \sqrt{x^{2}+y^{2}} \] \[ \nabla f(x, y)=7 \frac{x}{\sqrt{x^{2}+y^{2}}} i+7 \frac{y}{\sqrt{x^{2}+y^{2}}} j \] \(2 answers -
ASAP Plz
Find the gradient vector field \( \nabla f \) of \( f \) \[ f(x, y)=\frac{1}{7}(x-y)^{2} \] \[ \nabla f(x, y)= \]2 answers -
\( x=-(9 u+7 u v), y=5 u v-2 u v w \), and \( z=2 u v w \) implies \( \frac{\partial(x, y, z)}{\partial(u, v, w)}= \)2 answers -
\( x=9 w-(10 u+8 v), y=4 u+5 v+8 w \), and \( z=8 u+4 v+3 w \) implies \( \frac{\partial(x, y, z)}{\partial(u, v, w)}= \)2 answers -
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Find projwv. v = 23 + 3j, w - 8t - 67 2i 6j = OB O 1 0 (1-61) 25 (4i-3i) 4 325 (i - 6j) 13 (1-31)
Find \( \operatorname{proj}_{\mathrm{w}} \mathrm{v} \). \[ \begin{array}{l} v=2 i+3 j, w=8 i-6 j \\ -\frac{8}{5}(i-6 j) \\ -\frac{1}{25}(4 i-3 j) \\ -\frac{4}{325}(i-6 j) \\ -\frac{4}{13}(i-3 j) \end{2 answers -
Consider the following. \( \iint_{D} x y d A, \quad D \) is enclosed by the curves \( y=x^{2}, y=4 x \) Express \( D \) as a region of type I. \[ \begin{array}{l} D=\left\{(x, y) \mid 0 \leq x \leq 4,2 answers -
Find the maximum value of the function \( f(x, y)=x+y \) subject to the con-straint \( x^{2}+y^{4}=2 \).2 answers -
16. Determine whether the point is a source, sink, or incompressible. (a) \( \mathbf{F}(x, y, z)=\langle 2, y, 1\rangle \) (b) \( \mathbf{F}(x, y, z)= \) \( (2,2,1) \) \( \left(\frac{\pi}{2}, \pi, 4\r2 answers -
13. Evaluate \( \int_{S} \int f(x, y, z) d S \). (a) \( f(x, y, z)=x^{2}+y^{2}+z^{2} \) (b) \( f(x, y, z)=\sqrt{x^{2}+y^{2}+z^{2}} \) \( S: z=x+y, x^{2}+y^{2} \leq 1 \) \( S: z=\sqrt{x^{2}+y^{2}}, x^{2 answers -
Solve the initial value system \[ \begin{array}{l} x^{\prime}=-x+y ; x(0)=5 \\ y^{\prime}=9 x-y ; y(0)=-3 \end{array} \]0 answers