Calculus Archive: Questions from October 30, 2022
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Given line integral: \( \int_{C} f(x, y, z) d x+g(x, y, z) d y+h(z, y, z) d z=3 \) Evaluate: \[ \int_{C} f(x, y, z) d x+g(x, y, z) d y+h(z, y, z) d z \] Select one: A. \( -3 \) B. \( -3 / 2 \) C. \( -2 answers -
need help with 16,20,37and44 please
1-54 Use the guidelines of this section to sketch the curve. 31. \( y=\sqrt[1]{x^{2}-1} \) 2. \( y=2 x^{3}-12 x^{2}+18 x \) 33. \( y=\sin ^{3} x \) 32. \( y=\sqrt[3]{x^{3}+1} \) 1. \( y=x^{3}+3 x^{2}2 answers -
Solve the differential equation \[ \begin{aligned} x^{2} \frac{\mathrm{d} y}{\mathrm{~d} x} &+x y=2 x^{7}, \quad x>0 \\ y &=\frac{2}{7} x^{7}+C x \\ y &=\frac{2}{7} x^{7}+\frac{C}{x} \\ y &=\frac{2}{72 answers -
Use the chain rule to find the indicated derivative. \( \frac{\partial g}{\partial u} \), where \( g(u, v)=f(x(u, v), y(u, v)), f(x, y)=3 x^{2} y^{5}, x(u, v)=u \cos v, y(u, v)=u \sin v \) A. \( \frac2 answers -
Use the chain rule to find the indicated derivative. \( \frac{\partial g}{\partial u} \), where \( g(u, v)=f(x(u, v), y(u, v)), f(x, y)=3 x^{2} y^{5}, x(u, v)=u \cos v, y(u, v)=u \sin v \) \( \frac{212 answers -
Select the domain of the given function. \[ f(x, y, z)=\frac{6 z x}{\sqrt{14-x^{2}-y^{2}-z^{2}}} \] Domain \( =\left\{(x, y, z) \mid x^{2}+y^{2}+z^{2}14\right\} \) Domain \( =\left\{(x, y, z) \mid x^{1 answer -
Find the indicated partial derivatives. \[ f(x, y)=x^{8}+2 x y^{2}-4 y ; \frac{\partial^{2} f}{\partial x^{2}} ; \frac{\partial^{2} f}{\partial y^{2}} ; \frac{\partial^{2} f}{\partial x y} \] A. \( \f2 answers -
Solve the initial value problem. \[ \frac{d^{2} y}{d x^{2}}=4-7 x, y^{\prime}(0)=8, y(0)=2 \] A) \( y=2 x^{2}-\frac{7}{6} x^{3}+8 x+2 \) B) \( y=2 \) C) \( y=4 x^{2}+7 x^{3}+8 x+2 \) D) \( y=2 x^{2}+\2 answers -
Design an exercise that has to be solved using the l'Hopital rule. Show the solution process for the exercise. In the solution process you have to demonstrate why it is necessary to use l'Hopital and
Diseñe un ejercicio que tenga que ser resuelto utilizando la regla de l'Hopital. Muestre el proceso de solución para el cjercicio. En el proceso de solución tiene que demostrar por qué es necesari2 answers -
3. (mandatory) Show that \( U(x, y, z)=\frac{1}{\sqrt{x^{2}+y^{2}+z^{2}}} \) is a solution of \[ \frac{\partial^{2} U}{\partial x^{2}}+\frac{\partial^{2} U}{\partial y^{2}}+\frac{\partial^{2} U}{\part2 answers -
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find y'. show all steps
\( y=\left(\frac{\left.3 x^{2}-4 x+9\right)}{\left(2 x^{2}-4 x\right)}\right. \)2 answers -
6. Find the derivative \( y^{\prime} \) of the given function \( y \). (a) \( y=\frac{\sec (x)}{(3 x-5)^{6}} \) (b) \( y=\sqrt{2 x+1} \cdot(3 x-2)^{10} \)2 answers -
Find all values of \( x \) and \( y \) such that \( f_{x}(x, y)=0 \) and \( f_{y}(x, y)=0 \) simultaneously. \[ f(x, y)=x^{2}+3 x y+y^{2}-30 x-30 y+36 \] \[ (x, y)=(\quad) \]2 answers -
Evaluate the triple integral. \[ \iiint_{F} 5 y^{2} \cos (z) d V \text { where } F=\left\{(x, y, z) \mid 0 \leq y \leq \sqrt{\frac{\pi}{2}}, 0 \leq x \leq y, 0 \leq z \leq x y\right\} \]2 answers -
2 answers
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5. Differentiate the following: a) \( y=e^{x}\left(x^{3}+4\right) \) d) \( f(x)=e^{-4 x} \) b) \( y=x^{3} e^{x} \) e) \( g(x)=e^{x^{3}+8 x} \) \( y=\frac{e^{x}}{x^{2}} \) f) \( h(x)=e^{\sqrt{x^{2}+5}}2 answers -
Find all the second partial derivatives. \[ f(x, y)=\sin ^{2}(m x+n y) \] \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y)= \] \[ f_{y c}(x, y)= \] \[ f_{y y}(x, y)= \]2 answers -
2 answers
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Find the spherical coordinate expression for the function \( F(x, y, z) \). \[ F(x, y, z)=x^{5} y^{2} \sqrt{x^{2}+y^{2}+z^{2}} \] \[ f(\rho, \theta, \varphi)= \]3 answers -
Solve \( y^{\prime \prime}-16 y^{\prime}+66 y=\delta(t-7), \quad y(0)=y^{\prime}(0)=0 \) \( y(t)= \) Match each ODE with the graph of its respons \[ \begin{array}{l} y^{\prime \prime}+y=\delta\left(t2 answers -
\( \int_{-6}^{6} \int_{0}^{\sqrt{36-x^{2}}} f(x, y) d y d x=\int_{-\sqrt{36-y^{2}}} \) ห \( f(x, y) d x d y \)2 answers -
Find all the second partial derivatives. \[ f(x, y)=x^{6} y^{7}+6 x^{8} y \] \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y)= \] \[ f_{y x}(x, y)= \] \[ f_{y y}(x, y)= \]2 answers -
Differentiate the function. \[ y=\frac{6 x^{2}-5}{8 x^{3}+3} \] Differentiate the function. \[ y=\left(3 x^{2}-10\right)^{-14} \] \[ \frac{d y}{d x}= \]2 answers -
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Solve the following differential equations with the Laplace transform method: 1. \( y^{\prime \prime}+4 y=3 ; \quad y(0)=y \cdot(0)=0 \) 2. \( 4 y^{\prime}-2 y=t ; \quad y(0)=0 \) 3. \( y^{\prime \pri2 answers -
Given \( f(x, y)=5 x^{5}+6 x^{2} y^{4}-5 y^{3} \) \[ f_{x}(x, y)= \] \[ f_{y}(x, y)= \] \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y)= \]2 answers -
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Find \( y^{\prime} \) by implicit differentiation. Match the equations defining \( y \) implicitly with the letters labeling the expressions for \( y^{\prime} \). 1. \( 5 x \cos y+6 \cos 2 y=5 \sin y2 answers -
Solve the differential equation. 7. \( y^{\prime}-3 y=0 \) 8. \( y^{\prime}+4 y=2 \) 9. \( y^{\prime}+y \cos 2 x=\cos 2 x \) 10. \( x y^{\prime}+3 x y=6 x^{3}-4 x \) 11. \( y^{\prime}-2 t y=2 t \) 12.2 answers -
22,24,26,28,30,32,34
golve the initial-value problem. State an interval on pistich the solution exists. 21. \( y^{\prime}+4 y=6 ; y(0)=2 \) 22. \( x y^{\prime}+y=0 ; y(1)=3 \) 23. \( (1+\sin x) y^{\prime}+y \cos x=\cos x+2 answers -
solve the differential equation. Be sure to check for possible constant solutions. If necessary, write your answer implicitly. 2. \( 3 y^{2} \frac{d y}{d x}=5 x \) 1. \( \frac{d y}{d x}=4 x^{3} y \) 32 answers -
Differentiate. \[ y=\log _{7}\left(x^{4}+x\right) \] \[ \frac{d}{d x} \log _{7}\left(x^{4}+x\right)= \]2 answers -
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Calculate the limits if they exist
Calcule los siguientes límites, si es que existen: (a) \( \lim _{(x, y) \rightarrow(1,0)} \frac{x^{2}-y}{y-x y} \) (b) \( \lim _{(x, y) \rightarrow(0,0)} \frac{1-\cos \left(x^{2}+y^{2}\right)}{x^{2}+2 answers -
2 answers