Calculus Archive: Questions from June 10, 2023
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Let z = sin(5x + 4y³); Find vz. A vz = 22y³cos(5x + 4y³) i+ 15x²cos(5x + 4y³)j B vz = 15x³cos(5x + 4y³) i+ 22y²cos(5x4 + 4y³)j C 12y²cos(5x + 4y³) i+ 20x³cos(5x + 4y³)j D vz = 22x³cos(5x
\( \begin{array}{l}z=\sin \left(5 x^{4}+4 y^{3}\right) ; \text { Find } \nabla z \\ \nabla z=22 y^{3} \cos \left(5 x^{4}+4 y^{3}\right) i+15 x^{2} \cos \left(5 x^{4}+4 y^{3}\right) j \\ \nabla z=15 x^2 answers -
Find \( f^{\prime}(2) \) if \( f(x)=x^{3} \int_{2}^{x} \frac{\sin t}{t} d t \) A. \( 8 \sin 2 \) B. 12 C. \( 4 \sin 2 \) D. 8 E. 42 answers -
\[ \int 2 x \sin 3 x d x=? \] A. None of these B. \( 2\left(\frac{2}{3} x \cos 3 x-\frac{2}{9} \sin 3 x\right)+C \) C. \( 2\left(\frac{-2}{3} x \cos 3 x+\frac{2}{9} \cos 3 x\right)+C \) D. \( 2\left(\2 answers -
Suppose \( f \in C^{1} \), and define a function \( g(x, y)=\left(x^{2}+y^{2}\right) f\left(x^{2}+y^{2}\right) \). Show that \( g \) satisfies \( y \frac{\partial g}{\partial x}=x \frac{\partial g}{\p2 answers -
Solve* the 2 following questions
Solvel \( y^{\prime \prime}+5 y^{\prime}+4 y=0 \quad y(0)=y^{\prime}(0)=1 \) Solvel \( y^{\prime \prime}+4 y^{\prime}-2 y=0 \quad y(0)=1 \quad y^{\prime}(0)=-2 \)2 answers -
Find the derivative \( \frac{d y}{d x} \) (a) \( y=\cos (\gamma x) \cdot \tan ^{2}(7 x) \) (b) \( y=\ln (\gamma+\arctan (\gamma x)) \) (c) \( y=\cosh \left[\arcsin \left(\frac{x}{\gamma}\right)\right]2 answers -
Only B and C and why it doesnt exist the limit?
I. Determine el límite, en caso de que no exista explique por qué. a) \( \lim _{(x, y) \rightarrow(0,1)} \frac{\arccos (x / y)}{1+x y} \) b) \( \lim _{(x, y) \rightarrow(0,0)} \frac{x-y}{\sqrt{x}+\s2 answers -
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24. \( \iint_{R} \frac{1+x^{2}}{1+y^{2}} d A, \quad R=\{(x, y) \mid 0 \leqslant x \leqslant 1,0 \leqslant y \leqslant 1\} \)2 answers -
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Evalúa la integral e interprétala como el área de una región. |2 sen(x) − 2 cos(2x)| dx, de 0 a pi/22 answers
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Un circuito serie RC (con \( R=325 \Omega \) y \( C=2,000 \mu F \) ) es conectado a un voltaje de 10 Volts durante un tiempo de \( 2.4 \tau \). Calcule el voltaje al cual se cargó el capacitor0 answers -
Solve the following boundary-value problem: \( y^{\prime \prime}+9 y=0, ; y(0)=-1, y\left(\frac{\pi}{6}\right)=1 \) (A) \( y=\cos 3 x+\sin 3 x \) (B) \( y=-\cos 3 x+\sin 3 x \) (C) \( y=\cos 3 x-\sin2 answers -
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