Calculus Archive: Questions from June 12, 2023
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Change the order of integration \[ \int_{0}^{1} \int_{x}^{1} f(x, y) \mathrm{d} y \mathrm{~d} x \] \[ \int_{0}^{1} \int_{x}^{1} f(x, y) \mathrm{d} y \mathrm{~d} x \] \( " /> \) a. \[ \begin{array}{l}2 answers -
Change the erser of in \( \int_{0}^{1} \int_{0}^{\pi} f(z, 0) d y l s \) oi \[ \begin{array}{l} \int_{0}^{1} \int_{0}^{7} f(x, y) d x d y \\ \int_{1}^{7} f(x, y) d e d y \end{array} \] \[ \begin{array2 answers -
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Find partial derivatives \( f_{x}(x, y, z), f_{y}(x, y, z) \), and \( f_{z}(x, y, z) \). \[ f(x, y, z)=x e^{14 y}+y e^{3 z}+z e^{6 x} \] (Use symbolic notation and fractions where needed.) \[ f_{x}(x,2 answers -
Let \( f(x, y, z)=6 x y \sin (9 z)-2 y z \sin (7 x) \). Find \( f_{x}(x, y, z), f_{y}(x, y, z) \), and \( f_{z}(x, y, z) \). (Use symbolic notation and fractions where needed.) \( f_{x}(x, y, z)= \) \2 answers -
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\[ \int_{-3}^{1-e} \int_{1-x}^{4} f(x, y) d y d x+\int_{1-e}^{1} \int_{e}^{4} f(x, y) d y d x+\int_{1}^{\ln 4} \int_{e^{x}}^{4} f(x, y) d y d x=? \] A) \( \left.\left.\left.\int_{e}^{4} \int_{1-y}^{\l2 answers -
\[ \int_{-3}^{1-e} \int_{1-x}^{4} f(x, y) d y d x+\int_{1-e}^{1} \int_{e}^{4} f(x, y) d y d x+\int_{1}^{\ln 4} \int_{e^{x}}^{4} f(x, y) d y d x=? \] A) \( \left.\left.\int_{e}^{4} \int_{1-y}^{\ln y} f2 answers -
Find the equation of the tangent line of the parametric curve \( x=e^{\cos t}+3 t, y=e^{\text {sint }}+5 t \) at \( t=0 \). A) \( y=2 x-2 e+1 \) B) \( y=4 x+4 e-1 \) C) \( y=2 x-2 e-1 \) D) \( y=3 x-32 answers -
\[ \int_{-4}^{1-e} \int_{1-x}^{5} f(x, y) d y d x+\int_{1-e}^{1} \int_{e}^{5} f(x, y) d y d x+\int_{1}^{\ln 5} \int_{e^{x}}^{5} f(x, y) d y d x=? \] \[ \int_{e}^{4} \int_{1-y}^{\ln y} f(x, y) d x d y2 answers -
\[ \int_{-5}^{1-e} \int_{1-x}^{6} f(x, y) d y d x+\int_{1-e e}^{1} \int_{1}^{6} f(x, y) d y d x+\int_{1}^{\ln 6} \int_{e^{x}}^{6} f(x, y) d y d x=? \] A) \( \left.\left.\left.\left.\int_{e}^{\ln y} \i2 answers -
\[ \int_{-4}^{1-e} \int_{1-x}^{5} f(x, y) d y d x+\int_{1-e}^{1} \int_{e}^{5} f(x, y) d y d x+\int_{1}^{\ln 5} \int_{e^{x}}^{5} f(x, y) d y d x=? \] A) \( \left.\int_{e}^{4} \int_{1-y}^{\ln y} f(x, y)2 answers -
\( \int_{-4}^{1-e} \int_{1-x}^{5} f(x, y) d y d x+\int_{1-e}^{1} \int_{e}^{5} f(x, y) d y d x+\int_{1}^{\ln 5} \int_{e^{x}}^{5} f(x, y) d y d x=? \) \( \left.\left.\left.\left.\int_{e}^{4} \int_{1-y}^2 answers -
\[ \int_{-5}^{1-e} \int_{1-x}^{6} f(x, y) d y d x+\int_{1-e}^{1} \int_{e}^{6} f(x, y) d y d x+\int_{1}^{\ln 6} \int_{e^{x}}^{6} f(x, y) d y d x=? \] \( \left.\left.\left.\left.A) \int_{e}^{4} \int_{1-2 answers -
Very urgentt
\[ \int_{-4}^{1-e} \int_{1-x}^{5} f(x, y) d y d x+\int_{1-e}^{1} \int_{e}^{5} f(x, y) d y d x+\int_{1}^{\ln 5} \int_{e^{x}}^{5} f(x, y) d y d x \] toplamı aşağıdakilerden hangisine eşittir? A) \(2 answers -
\[ \int_{-5}^{1-e} \int_{1-x}^{6} f(x, y) d y d x+\int_{1-e e}^{1} \int_{e}^{6} f(x, y) d y d x+\int_{1}^{\ln 6} \int_{e^{x}}^{6} f(x, y) d y d x=? \] \( \left.\left.\left.\left.A) \int_{e}^{4} \int_{2 answers -
\[ \int_{-5}^{1-e} \int_{1-x}^{6} f(x, y) d y d x+\int_{1-e e}^{1} \int_{e}^{6} f(x, y) d y d x+\int_{1}^{\ln 6} \int_{e^{x}}^{6} f(x, y) d y d x=? \] \( \left.\left.\left.\left.A) \int_{e}^{4} \int_{2 answers -
\[ \int_{-4}^{1-e} \int_{1-x}^{5} f(x, y) d y d x+\int_{1-e}^{1} \int_{e}^{5} f(x, y) d y d x+\int_{1}^{\ln 5} \int_{e^{x}}^{5} f(x, y) d y d x=? \] \( \left.A) \int_{e}^{4} \int_{1-y}^{\ln y} f(x, y)2 answers -
\[ \int_{-3}^{1-e} \int_{1-x}^{4} f(x, y) d y d x+\int_{1-e}^{1} \int_{e}^{4} f(x, y) d y d x+\int_{1}^{\ln 4} \int_{e^{x}}^{4} f(x, y) d y d x=? \] A) \( \left.\left.\left.\int_{e}^{4} \int_{1-y}^{\l2 answers -
) f(x, y) -2 -1 2 2zy 2x 4y +4 y-1 Hiçbiri Leave blank m, 7 (x, y) = (1, 1) (x, y) = (1, 1) 1711400 Close
\( f(x, y)=\left\{\begin{array}{ll}\frac{2 x y-2 x-4 y+4}{y-1}, & (x, y) \neq(1,1) \\ m, & (x, y)=(1,1)\end{array}\right. \)0 answers -
\[ \begin{aligned} y^{\prime \prime}+5 y^{\prime}+6 y=2 x(t) ; y(0) & =1 \\ y^{\prime}(0) & =-1 \end{aligned} \] Using Laplace Transform2 answers -
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Q 3. Find the derivative of the following logarithmic functions. a) \( y=\ln \left(x^{3}+10 x^{2}+\sin x\right) \) b) \( y=\ln (\cos x \cdot \tan x) \) c) \( y=\ln \left(\frac{x^{2}+1}{x^{3}-4}\right)2 answers -
Q.6 Find the derivative of the inverse trigonometric functions. a) \( y=\sin ^{-1}(\ln x) \) b) \( y=\left[\cos ^{-1}\left(e^{3 x}\right)\right]^{4} \) c) \( y=\sec ^{-1}\left(\frac{x^{2}+1}{x-1}\righ2 answers -
Q. 2 Find the derivative of the following logarithmic functions. 1) \( y=\ln \left[\frac{\cot (10 x)}{4 x^{3}+10}\right] \) 2) \( y=\left[\ln \left(5 x^{4}-10 x^{3}+x^{2}-4\right)\right]^{\frac{1}{3}}2 answers -
Q. 5 Find the derivative of the inverse trigonometric functions. 1) \( y=\sin ^{-1}(\ln x) \) 2) \( y=\sec ^{-1}\left(\frac{x^{2}+1}{x-1}\right) \) 3) \( y=\tan ^{-1}[\ln (\cos (10 x))] \) 4) \( y=\le2 answers -
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1. Si \( f(x)=3^{x} \); hallar: a. \( v(x)=f(x)-1 \); traza su grafica e indica su Dominio y Campo de Valores Una fórmula para \( f^{-1}(x) \) y trazar la grafica de \( h(x)=f^{-1}(x-2)+1 \). Indica2 answers -
calculus derrivada
Sea \( f(x)=\frac{1}{x} \) a. (4 puntos) Use la definición de la derivada para mostrar que \( f^{\prime}(5)=-\frac{1}{25} \). b. (2 puntos) ¿Cuál es la ecuación de la recta tangente a la gráfica2 answers -
2. Halle el volumen del sólido acotado por \( z=10-\left(x^{2}+y^{2}\right), y=2 x, y=\frac{1}{2} x, z=0 \). Presente un dibujo claro y conciso que explique su región de integración. 3. Compute \[2 answers -
calculus
I. (6 puntos)Encuentre las asintotas horizontales y verticales de \( f(x)=\frac{x+4}{8-2 x-x^{2}} \cdot \measuredangle \) Que sucede con esta función cerca de \( x=2 ? \) Justifique su respuesta medi2 answers -
Calcule la solución general de la siguiente ecuación diferencial lineal homogénea de segundo orden: \[ y^{\prime \prime}+9 y^{\prime}+14 y=0 \]2 answers -
Calcule la solución particular de la siguiente ecuación diferencial lineal no homogénea de segundo orden: \[ 4 y^{\prime \prime}-8 y^{\prime}+3 y=0 \] considerando las siguientes condiciones inici2 answers -
Calcule la solución de la siguiente ecuación diferencial de segundo orden: \[ y^{\prime \prime}-y=0 \] sujeto a las siguientes condiciones iniciales: \( y(0)=2 \) and \( y^{\prime}(0)=-1 \)2 answers -
II. Analice la continuidad de la función a) f(x, y, z)=²+²-4 x²+y²−4 b) f(x, y) = sen (xy) xy # 0 XY 1, xy = 0
II. Analice la continuidad de la función a) \( f(x, y, z)=\frac{z}{x^{2}+y^{2}-4} \) b) \( f(x, y)=\left\{\begin{array}{c}\frac{\operatorname{sen}(x y)}{x y}, x y \neq 0 \\ 1, x y=0\end{array}\right.2 answers -
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b) y = x², x ≥ 0, y = 1, y = 4, revolved about the y axis c) y = 2x², x ≥ 0, the y axis, y = 2, revolved about the x axis
b) \( y=x^{2}, x \geq 0, y=1, y=4 \), revolved about the \( y \) axis c) \( y=2 x^{2}, x \geq 0 \), the \( y \) axis, \( y=2 \), revolved about the \( x \) axis2 answers