Calculus Archive: Questions from March 02, 2023
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if \( y=\frac{\cos x}{x} \), then \( y^{\prime}= \) and \( y^{\prime \prime}= \) Hence, \( x y^{\prime \prime}+2 y^{\prime}= \)2 answers -
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estas pendejo o que
At what point on the curve \[ x=t^{3}, y=3 t, z=t^{4} \] will be parallel to the \( 3 x+3 y-4 z= \)2 answers -
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Calculate the double integral. \[ \iint_{R} \frac{2\left(1+x^{2}\right)}{1+y^{2}} d A, R=\{(x, y) \mid 0 \leq x \leq 1,0 \leq y \leq 1\} \]2 answers -
Evaluate the integral. \[ \int \frac{\cos y d y}{\sin ^{2} y+2 \sin y-8} \] \[ \int \frac{\cos y d y}{\sin ^{2} y+2 \sin y-8}= \] (Type an exact answer.)2 answers -
I. Utilizando su calculadora determine: \( \log 3.2= \) \( \log 7= \) \( \log (5 * 4)= \) \( \log 6+\log 12= \) \( \log \left(\frac{5}{2}\right)= \) \( \log [13.4+3]= \) \( \log \left(\frac{13}{6} * 32 answers -
Evaluate the integral. \[ \int \frac{\cos y d y}{\sin ^{2} y+2 \sin y-24} \] \[ \int \frac{\cos y d y}{\sin ^{2} y+2 \sin y-24}= \] (Type an exact answer.)2 answers -
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Given the function \( f(x)=5 x^{2}-3 x+2 \), determine: a) \( \lim _{z \rightarrow x} \frac{f(z)-f(x)}{z-x} \) b) \( f^{\prime}(x) \) a) \( \lim _{z \rightarrow x} \frac{f(z)-f(x)}{z-x}= \) b) \( f^{\2 answers -
Pregunta 4 Evaluate the integral by using the adequate identity. \[ I=\int \sin (3 x) \sin (6 x) d x \] A. \( l=\frac{1}{4}\left[\sin 6 x-\frac{1}{3} \sin 3 x\right]+C \) B. \( I=\frac{1}{6}\left[\cos2 answers -
Determine the derivative for each: a) \( y=\left(x^{2}+1\right)\left(x^{3}+1\right) \) b) \( y=\sqrt{x}(2 x+3) \) c) \( y=\frac{3 x-1}{2 x+1} \) d) \( y=\frac{x^{4}}{1-x^{2}} \) \( y=\sqrt{\frac{x-1}{2 answers -
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(1 point) Find the gradient vector field of the following functions: \[ f(x, y, z)=3 \tan (-2 x-y z), \quad \nabla f(x, y, z)= \] \[ g(x, y, z)=x^{2}+7 x y z-\frac{z^{3}}{x}, \quad \nabla g(x, y, z)=2 answers -
(1 point) Find the gradient vector field of the following functions: \[ f(x, y)=x e^{-2 x y}, \quad \nabla f(x, y)= \] \[ g(x, y)=2 x \ln \left(2+y^{2}\right), \quad \nabla g(x, y)= \] \[ h(x, y)=3 \t2 answers -
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5. Let \( f(u, v)=\left(\cos v+u^{2}, e^{u+v}\right) \) and \( g(x, y)=\left(e^{x^{2}}, x-\sin y\right) \). (a) Find \( \mathbf{D} f(u, v) \) and \( \mathbf{D} g(x, y) \); (b) Find \( \mathbf{D}(f \ci2 answers -
7-18. Version 1 of the Chain Rule Use Version 1 of the Chain Rule to calculate \( \frac{d y}{d x} \) 7. \( y=(3 x+7)^{10} \) 8. \( y=\left(5 x^{2}+11 x\right)^{20} \) 9. \( y=\sin ^{5} x \) 10.) \( y=2 answers -
Find \( y^{\prime} \) and \( y^{\prime \prime} \). \[ y=e^{5 e^{x}} \] \( y^{\prime}= \) \( y^{\prime \prime}= \)2 answers -
Evaluate the integral. \[ \int_{-2}^{4} f(x) d x \text { where } f(x)=\left\{\begin{array}{ll} 4 & \text { if }-2 \leq x \leq 0 \\ 5-x^{2} & \text { if } 02 answers -
Find \( \frac{d^{2} y}{d x^{2}} \) \[ y=-3 x^{6}-5 \] \[ \frac{d^{2} y}{d x^{2}}= \] \( \begin{array}{l}\text { Find } \frac{d^{2} y}{d x^{2}} \\ \qquad y=\frac{4 x^{3}}{3}-2 x \\ \frac{d^{2} y}{d x^2 answers -
Q6.
Given \( f(x, y)=5 x^{4}+x^{2} y^{5}-2 y^{2} \) \[ f_{x}(x, y)= \] \[ f_{y}(x, y)= \] \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y)= \]2 answers -
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only number 5
Find \( f_{x}(x, y), f_{y}(x, y), f_{x}(-2,4) \), and \( f_{y}(4,-3) \). 5. \( f(x, y)=5 x+7 y \) 6. \( f(x, y)=2 x-5 x y \)2 answers -
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Determine \( y^{\prime} \) when 1. \( y^{\prime}=\frac{\sin x(3+\cos x)}{4-\cos x} \) \[ e^{y+\cos x}=4-\cos x . \] 2. \( y^{\prime}=\frac{\sin x(5+\cos x)}{4-\cos x} \) 3. \( y^{\prime}=\frac{\cos x(2 answers -
\( \lim _{x \rightarrow-1} \frac{x+1}{x^{2}+5 x+4} \) \( \left.\infty(-0.9|-0.94|-0.944)-1.001)^{-1.01}\right)-1.1 \)2 answers