Calculus Archive: Questions from February 23, 2023
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4. \( 15 x^{2} y^{4}+e^{x} \sin y+\left(20 x^{3} y^{3}+e^{x} \cos y+\frac{1}{y+1}\right) y^{\prime}=0 \)2 answers -
differential equation \( y^{\prime}=(4 x+2 y+3)^{2} \) \( y=\frac{(4 x+2 y+3)^{3}}{3}+c \) b. \( 4 x+2 y+3=\sqrt{2} \tan (2 \sqrt{2} x+c) \) \( y=\frac{(4 x+2 y+3)^{3}}{12}+c \) \( y=-\frac{(4 x+3)^{32 answers -
1. Find the relative extrema of \( f(x, y)=x^{2}+y^{2} \). 2. Find the extrema of \( f(x, y, z)=x^{2}+y^{2}+z^{2} \) subject to \( x+y+z=1 \).2 answers -
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Solve the below problem.
\( y^{\prime \prime}-4 y^{\prime}+4 y=0 \quad y^{\prime \prime}(1)=4, y^{\prime}(0)=0 \)2 answers -
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3. Find the derivative of (A) \( f(x)=2 x^{3}+3 x^{2} \) (F) \( y=\sqrt{\frac{x^{2}}{e^{x}}} \) (B) \( g(t)=\sqrt[3]{t}-t \) (G) \( f(t)=\sin (2 \pi t) \) (c) \( y=\frac{7}{2 x+1} \) (-1) \( s=3+\frac2 answers -
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Given \( f(x, y)=4 \sqrt{7 x^{5}+8 y+5 x y^{4}} \), find \[ f_{x}(x, y)=\frac{1}{2}\left(140 x^{4}+20 y^{4}\right)^{\frac{-1}{2}} \times \] \[ f_{y}(x, y)=\frac{1}{\left(16+40 x y^{3}\right)^{\frac{1}2 answers -
Solve the given initial-value problem. \[ \frac{d^{2} y}{d \theta^{2}}+y=0, \quad y(\pi / 3)=0, \quad y^{\prime}(\pi / 3)=8 \]2 answers -
Calculate \( \iint_{\mathcal{S}} f(x, y, z) d S \) For \[ y=3-z^{2}, \quad 0 \leq x, z \leq 5 ; \quad f(x, y, z)=z \] \[ \iint_{\mathcal{S}} f(x, y, z) d S= \]2 answers -
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Find the derivative. \[ y=\frac{4}{x}+5 \sec x \] \[ y=(\csc x+\cot x)(\csc x-\cot x) \] \[ y=\frac{\sin x}{8 x}+\frac{8 x}{\sin x} \]2 answers -
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Evaluate the double integral. \[ \iint_{D} 3 x \sqrt{y^{2}-x^{2}} d A, D=\{(x, y) \mid 0 \leq y \leq 3,0 \leq x \leq y\} \]2 answers -
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Find the Volume
\( \begin{array}{l}y=\sin (x), \quad y=0, \quad 0 \leq x \leq \pi ; \text { about } y=-4 \\ \int^{\pi}\left(\begin{array}{c}x\end{array}\right) d x\end{array} \)2 answers -
Find the volume
\( \begin{array}{l}y=\sin (x), \quad y=0, \quad 0 \leq x \leq \pi ; \text { about } y=-4 \\ \int^{\pi}\left(\begin{array}{c}x\end{array}\right) d x\end{array} \)3 answers -
\( \begin{array}{l}\text { Q9. } \int \sin x \cos x \ln (\cos x) d x \\ \text { Q11. } \int \frac{d x}{\sqrt{x^{2}-4 x}} \\ \text { Q13. } \int \tan ^{5} \theta \sec ^{3} \theta d \theta \\ \text { Q12 answers -
Find the derivative of each function.
\( \begin{array}{l}y=\sqrt{x} \cos \sqrt{x} \\ y=(\arcsin 2 x)^{2}\end{array} \) \( \begin{array}{l}y=\frac{1}{\sqrt[3]{x+\sqrt{x}}} \\ y=\sqrt{\sin \sqrt{x}} \\ y=e^{\cos x}+\cos \left(e^{x}\right)\2 answers -
Sea \( A=\{-4,-1,0,2,4,6\} \) y \( B=\{-3,-1,4,8,10\} \) al calcular \( A \cap B= \) \{\} \[ \{-4,-3,-1,0,2,4,6,8,10\} \] No está la resouesta correcta \[ \{-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10\} \] \(2 answers -
Problem 4 Find the gradient of the following functions: (a) \( f(x, y)=x^{2} y+x \sqrt{1+y} \) (b) \( g(x, y)=4 x^{3}-x y^{2} \) (c) \( h(x, y, z)=x \cos (y+2 z) \)2 answers -
Sea \( A=\{-4,-1,0,2,4,6\} \) y \( B=\{-3,-1,4,8,10\} \) al calcular \( A \cup B= \) \( \{-4,-3,-1,0,2,4,6,8,10\} \) \( \{-1,4\} \) \( \{-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9,10\} \) No está la respuesta c2 answers -
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1. Find \( d y / d x \) using appropriate rules. \( \begin{array}{l}y=(\sqrt[5]{6 x-7})(\ln (3 x-2)) \\ y=\left(\tan ^{-1}(x)\right)^{3 x}\end{array} \)2 answers -
2. Solve the following EXACT differential equations. (a) \( (\sin y+y \cos x) d x+[\sin x+x \cos y] d y=0 \) (b) \( \frac{y}{x} d x+(1+\ln (x y)) d y=0 \)2 answers -
Problem 4 Find the gradient of the following functions: (a) \( f(x, y)=x^{2} y+x \sqrt{1+y} \) (b) \( g(x, y)=4 x^{3}-x y^{2} \) (c) \( h(x, y, z)=x \cos (y+2 z) \)2 answers -
Calculate all four second-order partial derivatives of \( f(x, y)=\sin \left(\frac{4 x}{y}\right) \). \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y)= \] \[ f_{y x}(x, y)= \] \[ f_{y y}(x, y)= \]2 answers -
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Problem 21. Find all possible first order partial derivatives for each function below. 1. \( f(x, y)=x y \) 2. \( g(x, y)=x \cos (x y) \) 3. \( h(x, y)=x^{2} y+x y^{2}+e^{x} \) 4. \( w(x, y)=x y z+x^{2 answers -
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\( f(x, y)=\left(4 y^{2}-x^{2}\right) e^{-x^{2}-y^{2}} \) on the domain \( D=\left\{(x, y) \mid x^{2}+y^{2} \leq 2\right\} \)2 answers -
-et \( y=\ln \left(x^{2}+y^{2}\right) \). Determine the derivative \( y^{\prime} \) at the point \( \left(\sqrt{e^{8}-64}, 8\right) \). \[ y^{\prime}\left(\sqrt{e^{8}-64}\right)= \]2 answers -
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\[ \begin{array}{c} y=\log _{2}\left(e^{-x} \cos (\pi x)\right) \\ y^{\prime}=-\log _{2} e[\pi \tan (x+1)] \end{array} \] Need Help?2 answers