Calculus Archive: Questions from November 02, 2022
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5-12 Find the limit. v. \( \lim _{(x, y) \rightarrow(3,2)}\left(x^{2} y^{3}-4 y^{2}\right) \) 6. \( \lim _{(x, y) \rightarrow(5,-2)}\left(x^{2} y+3 x y^{2}+4\right) \) 7. \( \lim _{(x, y) \rightarrow(2 answers -
3. Find \( \frac{\partial T}{\partial r}, \frac{\partial^{2} T}{\partial r^{2}}, \frac{\partial T}{\partial \theta} \) and \( \frac{\partial^{2} T}{\partial \theta^{2}} \) for \( T(x, y)=x^{3} y^{3} \2 answers -
13 and 15 and 17
13-18 Show that the limit does not exist. 13. \( \lim _{(x, y) \rightarrow(0,0)} \frac{y^{2}}{x^{2}+y^{2}} \) 14. \( \lim _{(x, y) \rightarrow(0,0)} \frac{2 x y}{x^{2}+3 y^{2}} \) 15. \( \lim _{(x, y)2 answers -
Find \( Y(s) \) for the initial value problem \[ \begin{array}{l} y^{\prime \prime}-25 y=g(t), y(0)=5, y^{\prime}(0)=3, g(t)=\left\{\begin{array}{ll} 4 & t5 \end{array}\right. \\ \frac{5 s^{3}+3 s^{2}2 answers -
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Find the first partial derivatives of the function. \[ f(x, y, z)=3 x \sqrt{y z} \] \( f_{x}(x, y, z)= \) \[ f_{y}(x, y, z)= \] \[ f_{z}(x, y, z)= \]2 answers -
Find all the second partial derivatives. \[ f(x, y)=x^{4} y-4 x^{3} y^{2} \] \( f_{x x}(x, y)= \) \( f_{x y}(x, y)= \) \( f_{y x}(x, y)= \) \( f_{y y}(x, y)= \)2 answers -
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1. Use a table to express the values of each of these Boolean functions. (a) \( F(x, y, z)=\bar{z} \) (b) \( F(x, y, z)=\bar{x} y+y z \) (c) \( F(x, y, z)=x y z+\overline{(x y z)} \) (d) \( F(x, y, z)2 answers -
Find \( y \) as a function of \( t \) if \[ \begin{array}{l} y(0)=2, \quad y^{\prime}(0)=5 \\ y= \end{array} \]2 answers -
Resolve the following first order differential equation
P7). Resuelva el siguiente P.V.I. 1. \( \left(x^{2}+1\right) \frac{d y}{d x}+3 x(y-1)=0, y(0)=2 \)2 answers -
Solve the following IVPs: (3.1) \( 6 y^{\prime \prime}+y^{\prime}-y=0, \quad y(0)=-1, \quad y^{\prime}(0)=2 \) (3.3) \( \quad y^{\prime \prime}-2 y^{\prime}+5 y=0, \quad y(-1)=0, \quad y^{\prime}(-1)=1 answer -
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Let \( f(x, y)=x^{2} y+x \ln (y) \) and \( g(x, y)=\left(2 x y, x^{2}+y^{2}\right) \). Calculate \( D(f \circ g)(1,-1) \).2 answers -
help asap
\( y^{(I V)}-16 y^{\prime \prime}+64 y=0 \) \( y^{(I V)}+625 y=0 \) \( \left(D^{4}-81\right) y=0 \) \( 6 y^{\prime \prime}-y^{\prime}-y=0 \)2 answers -
HELP PLS
Method of Variation of Parameters \[ \begin{array}{l} y^{\prime \prime}+y^{\prime}-6 y=\frac{1}{e^{x}-3} \\ \left(D^{2}+1\right) y=\sec ^{2} x \\ y^{\prime \prime}-10 y^{\prime}+25 y=\frac{1}{e^{9 x}+2 answers -
Find the derivative of the following: 1a) \( y=\frac{x+29}{x+0} \) b) \( y=\left(\frac{x+19}{x-5}\right)^{2} \) c) \( y=\tan (4 x-19 \cos (x)) \)2 answers -
solución particular de la ED \( y^{\prime \prime}+2 y^{\prime}+2 y=3 e^{-x}+2 e^{-x} \cos x+4 x^{2} e^{-x} \sin x \) es de la form a. \( y_{p}=A e^{-x}+\left(B x^{2}+C x+D\right) e^{-x} \cos x+\left(0 answers -
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Suppose that \( f^{\prime}(x)=2 x \) for all \( x \) a) Find \( f(-4) \) if \( f(0)=0 \) b) Find \( f(-4) \) if \( f(3)=7 \) c) Find \( f(-4) \) if \( f(-1)=6 \)2 answers -
answer all the questions pleas.
Q3: Evaluate the integral \[ \int \sin ^{2} x \cos ^{3} x d x \quad \int \sin ^{3} x \cos ^{2} x d x . \quad \int \cos ^{3} x \sin x d x \quad \int_{0}^{3-} \sin ^{5} x d x: \quad \int_{0}^{\pi / 2}(22 answers -
1. Find \( \partial y / \partial x_{1} \) and \( \partial y / \partial x_{2} \) for each of the following functions: (a) \( y=2 x_{1}^{3}-11 x_{1}^{2} x_{2}+3 x_{2}^{2} \) (c) \( y=\left(2 x_{1}+3\rig2 answers -
Solve \( (\cos x \cos y-\cot x) d x-(\sin x \sin y) d y=0 \) \( \cos y \sin x+\ln |\cos x|=c \) \( \cos y \sin x-\ln |\cos x|=c \) \( \cos y \sin x-\ln |\sin x|=c \) \( \cos y \sin x+\ln |\sin x|=c \)2 answers -
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