Calculus Archive: Questions from May 08, 2023
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Suppose \( f(x)=h(g(x) k(x)) \). If \( g(1)=4, k(1)=0, h(1)=-7, g^{\prime}(1)=3, k^{\prime}(1)=-6, h^{\prime}(1)=6 \), and \( h^{\prime}(0)=2 \), find \( f^{\prime}(1) \) Answer: \( f^{\prime}(1)= \)2 answers -
If \( \begin{aligned} f(x) & =\int_{0}^{\sin x} \sqrt{1+1^{2}} \\ g(y) & =\int_{3}^{y} f(x)\end{aligned} \)2 answers -
Q.29-31
27-34 Calculate the double integral. 27. \( \iint_{R} x \sec ^{2} y d A, \quad R=\{(x, y) \mid 0 \leqslant x \leqslant 2,0 \leqslant y \leqslant \pi / 4\} \) 28. \( \iint_{R}\left(y+x y^{-2}\right) d2 answers -
1) Determine el resultado de la siguiente anti-derivada \[ f^{\prime}(x)=\cos (x)-4 x+2 \] 2) \( y^{\prime}=\int\left(-5 x^{2}+\sec ^{2}(x)\right) d x \) 3) \( \int_{0}^{4}\left(\frac{2}{5} x^{2}+4 e^2 answers -
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utilizar una integral iterada para calcular el area de la region limitada
2. Utilizar un a integral iterada para calcular el área de la región limitada \[ x y=9, y=x, y=0, x=9 \] "Dibuja la región - cálcula el área2 answers -
Escribe y evalua la integral doble CP son coordenadad polares
Utilizar C. P. para escribir y evaluar la ID. (integral doble). \[ \iint_{R} f(x, y) d A \] donde \[ \begin{aligned} f(x, y)=e^{-\frac{\left(x^{2}+y^{2}\right)}{2}} ; R & =x^{2}+y^{2} \geq 25 \\ & x \2 answers -
1 h→0 hx+h 1 For x = 0, if y = lim then y(4)= - X
For \( x \neq 0 \), if \( y=\lim _{h \rightarrow 0} \frac{1}{h}\left(\frac{1}{x+h}-\frac{1}{x}\right) \), then \( y(4)= \)2 answers -
(1) \( \int\left(4 x^{3}-9 x^{2}+7 x+3\right) e^{-x} \cdot d x= \) A) \( e^{-x}\left[4 x^{3}+3 x^{2}+13 x+16\right]+C \) B) \( -e^{-x}\left[4 x^{3}+3 x^{2}+13 x+16\right]+C \) C) \( e^{-x}\left(4 x^{32 answers -
Let \( \vec{F}(x, y, z)=x^{2} \vec{i}-\cos (x y)(\vec{i}+\vec{j}) \). Calulate the divergence: \( \operatorname{div} \vec{F}(x, y, z)= \)2 answers -
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Consider the system of non-linear differential equations \[ \begin{array}{l} \frac{d x}{d t}=x \sin y \\ \frac{d y}{d t}=y \cos x \end{array} \] Select the option that gives the Jacobian matrix for th2 answers -
Let F(x, y, z) = x²i – cos(xz) (i + k). Calulate the divergence: div F(x, y, z) =
Let \( \vec{F}(x, y, z)=x^{2} \vec{i}-\cos (x z)(\vec{i}+\vec{k}) \). Calulate the divergence: \[ \operatorname{div} \vec{F}(x, y, z)= \]2 answers -
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derivatives
\( y=\sqrt{\cos x} \) \( y=x\left(x^{2}+1\right)^{13} \) \( y=(\cos 2 x+\sin 2 x)^{-2} \) \( y=(\cos x)^{\sqrt{2}} \)2 answers -
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Given \( f(x, y, z)=\sqrt{2 x+6 y+4 z} \) \[ f_{x}(x, y, z)= \] \[ f_{y}(x, y, z)= \] \[ f_{z}(x, y, z)= \]2 answers -
6. Find the derivative of the following. a. \( p(t)=12 t^{4}-6 \sqrt{t}+\frac{5}{t} \) h. \( r(t)=\frac{3 t-8}{(5-3 t)^{5}} \) b. \( y=\left(4 x^{5}-7 x\right)\left(x^{3}+2 x-3\right) \) i. \( y=-3 \s2 answers -
i need help as soon as possible Find the derivative of the following functions. a. y = tan x sinx d. y = x²-3 √x+2 cost b. y = 1+ sint e. y = csc((t² + 1)³) c. y = 0² sec 0 f. y = cot²(√w)
Find the derivative of the following functions. a. \( y=\tan x \sin x \) b. \( y=\frac{\cos t}{1+\sin t} \) c. \( y=\theta^{2} \sec \theta \) d. \( y=\sqrt{\frac{x^{2}-3}{x+2}} \) e. \( y=\csc \left(\2 answers -
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1) (12 ptos) Determine el resultado de la siguiente anti-derivada \[ f^{\prime}(x)=\operatorname{sen}(x)-2 x+6 \]2 answers -
Determine los resultados de la siguiente antiderivada.
\( \int_{0}^{4}\left(\frac{1}{3} x^{2}-6 e^{x}\right) d x \)2 answers -
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5) (24 ptos) Determine las anti-derivadas de las siguientes ecuaciones: a. \( f(x)=3 e^{5 x}+4 x \) b. \( f(x)=\log _{7} \frac{8 x^{2}}{e^{x}} \) c. \( f(x)=\ln (7 x)^{3}-e^{x^{2}}+\pi \) d. \( s(r)=\2 answers -
6) (15 ptos) \( \frac{d y^{2}}{d x^{2}}=3 x-5 \), con las siguientes condiciones iniciales \( \frac{d y}{d x}=3 \), \( \operatorname{con} x=0 \mathrm{y} \) \[ y=2, \operatorname{con} x=0 \text {. } \]2 answers -
Solve the differential equation (Hint: Use separable equations), \[ \frac{d y}{d \theta}=\frac{e^{y} \sin ^{2} \theta}{y \sec \theta} \] A. \( -e^{y}(y+1)=\frac{1}{3} \sin ^{3} \theta+C \) B. \( -e^{y2 answers -
Solve the initial-value linear differential equation, \[ 2 x \frac{d y}{d x}+y=6 x, \quad x>0, \quad y(4)=20 \] A. \( y=2 x+\frac{24}{x} \) B. \( y=2 x+\frac{24}{\sqrt{x}} \) C. \( y=2 x+24 \) D. \( y2 answers -
3. Trazar la curva representada por las ecuaciones paramétricas, indicar la orientación de la curva y escriba la ecuación rectangular correspondiente eliminando el parámetro t. (16 puntos) \[ x=\s2 answers -
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