Calculus Archive: Questions from November 22, 2022
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3. Un factor integrante de la ecuación diferencial lineal \( x^{2} y^{\prime}+x(x+2) y=e^{x} \) es: a) \( x^{2} \) b) \( e^{x} \) c) \( x^{2} e^{x} \) d) \( e^{\frac{x^{3}}{3}+\frac{x^{2}}{2}} \) e)2 answers -
1. Resuelve los siguientes Problemas de Valor Inicial a) [7 pts.] \( x^{2} \frac{d y}{d x}=y(1-x) ; y(-1)=-1 \). b) \( [11 \) pts \( ] x \frac{d y}{d x}+y=4 x+1 ; y(1)=8 \). 2. [9 pts.] Verifica si la2 answers -
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1. Resuelve los siguientes Problemas de Valor Inicial b) \( [\mathbf{1 1} \mathbf{p t s}] x \frac{d y}{d x}+y=4 x+1 ; y(1)=8 \).2 answers -
2. [9 pts.] Verifica si la E.D. \( \left(y^{2} \cos x-3 x^{2} y-2 x\right) d x+\left(2 y \sin x-x^{3}+\ln y\right) d y=0 \) es exacta, y de ser así resuélvela.2 answers -
3. [8 pts.] Halla la solución de las siguientes ecuación diferencial \( \frac{d y}{d x}=1+e^{y-x+5} \).2 answers -
\[ \lim _{x \rightarrow 0} \frac{\tan x-\sin x}{\sin ^{3} x}=? \] (a) \( -1 / 2 \) (b) 0 (c) \( 1 / 2 \) (d) 1 (e) \( 3 / 2 \)2 answers -
Evaluate \( \iiint_{E}(x+y-2 z) d V \) where \[ E=\left\{(x, y, z) \mid-2 \leq y \leq 0,0 \leq x \leq y, 02 answers -
Find the derivatives of the following functions; a) \( y=\sqrt{x^{2}+3 x+4} \) b) \( y=\ln \left(7 x^{2}+2 x+10\right) \) c) \( y=x^{2} e^{x^{2}} \) d) \( y=\frac{\sin \left(4 x^{2}\right)}{\cos \left2 answers -
Express the integral \( \iiint_{E} f(x, y, z) d V \) as an iterated integral in six different ways, where \( \mathrm{E} \) is the solid bounded by \( z=0, x=0, z=y-3 x \) and \( y=6 \). \[ \begin{arra2 answers -
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Evaluate \( \iiint_{B} f(x, y, z) d V \) for the specified function \( f \) and \( \mathcal{B} \) : \[ f(x, y, z)=\frac{z}{x} \quad 2 \leq x \leq 6,0 \leq y \leq 9,0 \leq z \leq 10 \] \[ \iiint_{B} f(2 answers -
Evaluate \( \iiint_{\mathcal{W}} f(x, y, z) d V \) for the function \( f \) and region \( \mathcal{W} \) specified: \[ f(x, y, z)=6(x+y) \quad \mathcal{W}: y \leq z \leq x, 0 \leq y \leq x, 0 \leq x \2 answers -
Calculate the double integral: (a) \( \iint_{R}\left(y+x y^{-2}\right) d A, R=\{(x, y) \mid 0 \leq x \leq 2,1 \leq y \leq 2\} \) (b) \( \iint_{R} \frac{x y^{2}}{x^{2}+1} d A, R=\{(x, y) \mid 0 \leq x1 answer -
Evaluate the double integral. \[ \iint_{D} \frac{y}{x^{2}+1} d A, \quad D=\{(x, y) \mid 0 \leq x \leq 6,0 \leq y \leq \sqrt{x}\} \]2 answers -
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SQLE TEIE TINTTIMALI VALUR PROBLEMA \[ \begin{array}{l} y^{11}+y=g(t) \quad g(t)=\left\{\begin{array}{l} t \text { if } 0 \leq t \leq 4 \\ 0 \text { if } 4 \leq t \end{array}\right. \\ y(0)=0 \quad y^2 answers -
(20 puntos, 5c/u) Formule la integral definida que represente el área y calcule cada área a. b. \[ f(x)=4-2 x \] c. \[ f(x)=4-|x| \] d.2 answers -
\( \lim _{x \rightarrow 0}\left(\frac{\tan 5 x}{x^{3}}+\frac{a}{x^{2}}+\frac{\sin b x}{x}\right)=8 \) \( a= \) \( b=\quad \)2 answers -
3. (20 puntos, \( 5 \mathrm{c} / \mathrm{u} \) ) Sabiendo que \( \int_{0}^{5} f(x) d x=10 \) y \( \int_{5}^{7} f(x) d x=3 \) Calcular: a. \( \quad \int_{0}^{7} f(x) d x \) b. \( \quad \int_{5}^{0} f(x2 answers -
Express the integral \( \iiint_{E} f(x, y, z) d V \) as an iterated integral in six different ways, where \( E \) is the solid bounded by \( z=0, z=5 y \) and \( x^{2}=16-y \) \[ \begin{array}{l} 1 \i2 answers -
Given \( f(x, y)=2 x^{3}+x^{2} y^{5}-6 y^{4} \) \[ f_{x}(x, y)= \] \( f_{y}(x, y)= \) \( f_{x x}(x, y)= \) \( f_{x y}(x, y)= \)2 answers -
find the derivative of the following functions: Questions #32, #36, #38, #40, #42, #44
Find the derivative of each function. 1. \( y=\ln (8 x) \) 2. \( y=\ln (-4 x) \) 3. \( y=\ln (8-3 x) \) 4. \( y=\ln \left(1+x^{3}\right) \) 5. \( y=\ln \left|4 x^{2}-9 x\right| \) 6. \( y=\ln \left|-82 answers -
Questions #12, #14, #16, #22, #24, #26
Find the derivatives of the functions defined as follows. 1. \( y=\frac{1}{2} \sin 8 x \) 2. \( y=-\cos 2 x+\cos \frac{\pi}{6} \) 3. \( y=12 \tan (9 x+1) \) 4. \( y=-4 \cos \left(7 x^{2}-4\right) \) 52 answers -
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\[ y=2 \sin (x), \quad y=\mathrm{e}^{x}, \quad x=0, \quad x=\frac{}{2} \] Find the area of the region.2 answers -
Question 34
Find derivatives of the functions defined as follows. 1. \( y=e^{4 x} \) 2. \( y=e^{-2 x} \) 3. \( y=-8 e^{3 x} \) 4. \( y=1.2 e^{5 x} \) 5. \( y=-16 e^{2 x+1} \) 6. \( y=-4 e^{-0.3 x} \) 7. \( y=e^{x2 answers -
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Find the spherical coordinate expression for the function \( F(x, y, z) \). \[ F(x, y, z)=x^{3} y^{3} \sqrt{x^{2}+y^{2}+z^{2}} \] \[ f(\rho, \theta, \varphi)= \]3 answers -
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SOLVE USING MATLAB ONLY.
3. Solve the differential equation : \( \frac{d^{2} y}{d x^{2}}=\sin (6 x)-2 y \) \( y(0)=0, \quad y^{\prime}(0)=1 \)2 answers -
SOLVE USING MATLAB ONLY.
4. Solve the differential equation : \[ \begin{array}{l} \frac{d^{2} y}{d x^{2}}=\sin (5 x)-2 y \\ y(0)=1, \quad y^{\prime}(0)=1 \end{array} \]2 answers -
SO[O, I \( (\angle U \mid J) \) 1. \( \lim _{x \rightarrow 3^{+}} f(x)= \) 2. \( \lim _{x \rightarrow 3^{-}} f(x)= \) 3. \( \lim _{x \rightarrow 3} f(x)= \) 4. \( \lim _{x \rightarrow-1^{-}} f(x)= \)2 answers -
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Let \( F(x, y, z)=\left(3 x z^{2},-x y z, 6 x y^{3} z\right) \) be a vector field and \( f(x, y, z)=x^{3} y^{2} z \). \( \nabla f=(\quad) \). \[ \begin{array}{l} \nabla \times F=( \\ F \times \nabla f1 answer -
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HELP ASAP WILL RATE((:
Given \( f(x, y)=-5 x^{6}+x y^{5}+4 y^{3} \) \[ f_{x}(x, y)= \] \[ f_{y}(x, y)= \]2 answers -
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