Calculus Archive: Questions from September 22, 2022
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ve: \( y(9 x-2 y) d x-x(6 x-y) d y=0 \) \[ \begin{array}{l} x^{2}(y-3 x)=C y^{2} \\ y^{2}(x-3 y)=C x^{2} \\ y^{2}(y-3 x)=C x^{2} \\ x^{2}(x-3 y)=C y^{2} \end{array} \]1 answer -
interchangable DE 2&5 only
2. \( -\left(y^{2}+x^{2} y \sin x\right) d x+\left(x y+x^{2}\right) d y=0 \) 3. \( x d y+y d x=0 \) 4. \( x^{2} \cos ^{2}\left(\frac{y}{x}\right) \cos (x y)(x d y+y d x)-(y d x-x d y)=0 \) 5. \( (x d2 answers -
plz solve the following ODE,s
1. \( x \frac{d y}{d x}=4 y, \quad y(1)=1 \) 2. \( y^{\prime}+3 x^{2} y=x^{2} \) 3. \( (y+x) d y=(y-x) d x \) 4. \( x y^{\prime}+y=\frac{1}{y^{2}} \). 5. \( y^{\prime}=2+\sqrt{y-2 x+3} \) 6. \( 4 \fra1 answer -
Solve the following differential equations : \[ \begin{array}{l} 1-\quad\left(2 y^{2}+3 x\right) d x+2 x y d y=0 \\ 2-\quad y(x+y+1) d x+(x+2 y) d y=0 \\ 3-\quad 6 x y d x+\left(4 y+9 x^{2}\right) d y2 answers -
Solve the following differential equations: a) \( y^{\prime}=\csc x-y \cot x \) b) \( y^{\prime}=x-3 y \) c) \( y^{\prime}=x-2 x y \) d) \( y^{\prime}=x-2 y \cot 2 x \)2 answers -
Solve the following differential equations : a) \( y^{\prime}=y-x y^{3} e^{-2 x} \) b) \( x y^{\prime}-y=x^{3} y^{2} \)1 answer -
in \( y d A \), where \( R=\{(x, y) \mid 0 \leq y \leq x, 0 \leq x \leq \pi\} \). \[ 2+2 \pi^{2} \] \[ 2+\frac{1}{2} \pi^{2} \] \[ \frac{1}{2}+\pi^{2} \] \[ \frac{1}{2}+\frac{1}{2} \pi^{2} \] None of2 answers -
If \( \sin x=-\frac{1}{5} \) and \( \tan y=\frac{2}{5} \) where \( x \) and \( y \) are in the interval \( [\pi / 2,3 \pi / 2] \), What are the exact values of the following trigonometric ratios? (Mat1 answer -
2 answers
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Given \( f(x, y, z)=\sqrt{5 x^{2}+6 y^{2}+z^{2}} \) \( f_{x}(x, y, z)= \) \[ f_{y}(x, y, z)= \] \[ f_{z}(x, y, z)= \]2 answers -
2 answers
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Given \( f(x, y)=6 x^{2}+1 x y^{4}-6 y^{5} \), find the following numerical values: \[ f_{x}(3,3)= \] \[ f_{y}(3,3)= \]2 answers -
Given \( f(x, y, z)=\sqrt{4 x^{2}+5 y^{2}+6 z^{2}} \) \[ f_{x}(x, y, z)= \] \( f_{y}(x, y, z)= \) \[ f_{z}(x, y, z)= \]2 answers -
Given \( f(x, y, z)=\sqrt{-3 x-5 y+z} \), \( f_{x}(x, y, z)= \) \( f_{y}(x, y, z)= \) \( f_{z}(x, y, z)= \)2 answers -
2 answers
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2 answers
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Given \( f(x, y)=2 x^{5}+x^{2} y^{6}-4 y^{3} \) \( f_{x}(x, y)= \) \( f_{y}(x, y)= \) \( f_{x x}(x, y)= \) \( f_{x y}(x, y)= \)2 answers -
solve 32, 35, and 38
29. \( \lim _{x \rightarrow 2^{+}} e^{3 /(2-x)} \) 30. \( \lim _{x \rightarrow 2^{-}} e^{3 /(2-x)} \) 31. \( \lim _{x \rightarrow \infty}\left(e^{-2 x} \cos x\right) \) 32. \( \lim _{x \rightarrow(\pi1 answer -
Consider w, x and y to determine dw/dr & dw/dØ
1. Considere \( w=x^{2}-2 x y+y^{2}, x=r+\theta, y=r-\theta \) para determinar \( \frac{\partial w}{\partial r} \& \frac{\partial w}{\partial \theta} \)2 answers -
\[ \int_{R}^{\infty} x y e^{x y^{2} / 81} d A \] where \( R=\{(x, y) \mid 0 \leq x \leq 2,0 \leq y \leq 9\} \)2 answers -
Differentiate the following function. \[ g(x)=3\left(x^{3}-6\right)^{2}\left(x^{2}+4 x-6\right)^{10} \] A) \( g^{\prime}(x)=30(2 x+4)\left(x^{3}-6\right)^{2}\left(x^{2}+4 x-6\right)^{9}+18 x^{2}\left(2 answers -
2 answers
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I. find the total differentiation II. Considere the function a) evaluate b)calculate c) use the total differentiation dz to aproximate z
I. Halle el diferencial total a) \( z=e^{x} \operatorname{sen}(y) \) b) \( w=\frac{x+y}{z-3 y} \) II. Considere la función \( f(x, y)=y e^{x} y \) trabaje: a) Evaluar \( f(2,1) \) y \( f(2.1,1.05) \)2 answers -
Differentiate the following function. \[ g(x)=3\left(x^{3}-6\right)^{2}\left(x^{2}+4 x-6\right)^{10} \] A) \( g^{\prime}(x)=30(2 x+4)\left(x^{3}-6\right)^{2}\left(x^{2}+4 x-6\right)^{9}+18 x^{2}\left(2 answers -
Compute \( f_{x} \) for \( f(x, y)=2 x^{3}+5 y^{2}+3 x y \) Compute \( f_{y} \) for \( f(x, y)=2 x^{3}+5 y^{2}+3 x y \)2 answers -
2 answers
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1 answer
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Find \( d y \) i \( d x \) if 1) \( y=3 x^{3}-2 \sqrt{x}+x-3 \) 2) \( y=\frac{3}{(2 x)^{3}}+2 \sin x \) 3) \( y=\frac{2}{\sqrt[3]{x}}-3 \cos x \) 4) \( y=\frac{3 x^{2}+2 x-\sqrt{x}}{x} \) 5) \( y=x^{21 answer -
1 answer
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If \( \sin x=-\frac{1}{4} \) and \( \tan y=\frac{2}{3} \) where \( x \) and \( y \) are in the interval \( [\pi / 2,3 \pi / 2] \), What are the exact values of the following trigonometric ratios? (Mat2 answers -
please show your work
Find \( d y / d x \) if 1) \( y=3 x^{3}-2 \sqrt{x}+x-3 \) 2) \( y=\frac{3}{(2 x)^{3}}+2 \sin x \) 3) \( y=\frac{2}{\sqrt[3]{x}}-3 \cos x \) 4) \( y=\frac{3 x^{2}+2 x-\sqrt{x}}{x} \) \( y=x^{2}\left(32 answers -
solve the differential equations
\( 6 x+y^{\prime}=4 y x \) \( y^{\prime}=\frac{6 x+\ln (x)}{y^{3}} \)2 answers -
please show your work Find dy/dx if:
3) \( y=\frac{2}{\sqrt[3]{x}}-3 \cos x \) 4) \( y=\frac{3 x^{2}+2 x-\sqrt{x}}{x} \) 5) \( y=x^{2}\left(3 x^{3}+5 x^{2}\right) \)1 answer -
Compute \( f_{x} \) for \( f(x, y)=2 x^{3}+5 y^{2}+3 x y \) Compute \( f_{y} \) for \( f(x, y)=2 x^{3}+5 y^{2}+3 x y \)2 answers -
Evaluate the integral \( \int_{0}\left[\left(3 t e^{7 t^{2}}\right) \mathbf{i}+\left(6 e^{-6 t}\right) \mathbf{j}+(1) \mathbf{k}\right] \mathrm{dt} \) \[ \int_{0}^{1}\left[\left(3 t e^{7 t^{2}}\right)1 answer -
1 point iolve the equation: \( y^{\prime}+2 y=2 e^{x} \) \[ \begin{array}{l} y=\frac{2}{3} e^{-2 x}+C e^{-x} \\ y=\frac{2}{3} e^{x}+C e^{-2 x} \\ y=C e^{x}+\frac{2}{3} e^{-2 x} \\ y=e^{x^{2}}+C e^{x}2 answers -
Solve 41 please
In Exercises 41-49, determine the global extreme values of the function on the given 41. \( f(x, y)=x^{3}-2 y, \quad 0 \leq x \leq 1, \quad 0 \leq y \leq 1 \) 42. \( f(x, y)=5 x-3 y, \quad y \geq x-2,2 answers -
Solve 47 please
In Exercises 41-49, determine the global extreme values of the function on the given 41. \( f(x, y)=x^{3}-2 y, \quad 0 \leq x \leq 1, \quad 0 \leq y \leq 1 \) 42. \( f(x, y)=5 x-3 y, \quad y \geq x-2,2 answers -
(c) \[ y=\ln \left(\sin \left(x^{2}+5\right)\right) \] (d) \[ y=(\ln x)(\sin x)\left(x^{2}+5\right) \]0 answers