Calculus Archive: Questions from February 02, 2023
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y =x³-3x²-6x +1 x=-1 a) y=3x+6 b) y=3x+6 c) y=3x-6 d) y=-3x -6
Ejercicio (5 puntos para las asignaciones): Encuentre la ecuación de la recta tangente a la curva \( y=x^{3}-3 x^{2}-6 x+1 \) en \( x=-1 \) A) \( y=3 x+6 \) B) \( y=-3 x+6 \) C) \( y=3 x-6 \) D) \( y2 answers -
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Find the derivative of each. 1. \( y=x \cdot \ln \left(x^{3}\right) \quad x>0 \) 2. \( y=\frac{1}{(\ln (2 x))^{5}} \quad x>0 \) 3. \( y=e^{-10 x^{2}} \)2 answers -
7) On a separate paper, sketch the following plots: i. \( y=\frac{1}{x} \) ii. \( y=\frac{1}{x^{2}} \) iii. \( y=e^{x} \) iv. \( y=e^{-x} \) v. \( \quad y=\ln x \) vi. \( y=\ln e^{x} \) vii. \( y=(x-32 answers -
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3 answers
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For each vector field \( \vec{F}(x, y, z) \), compute the curl of \( \vec{F} \) and, if possible, find a function \( f(x, y, z) \) so that \( \vec{F}=\nabla f \). If no such function \( f \) exists, e4 answers -
Given \( f(x, y)=3 x^{9} \cos \left(y^{7}\right) \), find \[ f_{x y}(x, y)=-189 x^{8} y^{6} \sin \left(y^{7}\right) \] \( \sigma^{6} \) \[ f_{y y}(x, y)= \]2 answers -
\[ (x, y) \rightarrow(0,0) \Rightarrow\left(x^{3}-5 y^{4}+\pi\left(x^{2}+y^{2}\right)\right) /\left(x^{2}+y^{2}\right) \rightarrow \] a. 1 b. 0 c. va a parar \( \pi^{3} \) d. Ninguno de los otros valo2 answers -
Evalúe las integrales usando el método de integración por partes. (20 Puntos a) \( \int r e^{r / 2} d r \) b) \( \int x^{2} \operatorname{Cos}(m x) d x \) c) \( \int e^{-\theta} \operatorname{Cos}(2 answers -
(1 point) Calculate \( \iint_{\mathcal{S}} f(x, y, z) d S \) For \[ \begin{array}{l} y=7-z^{2}, \quad 0 \leq x, z \leq 9 ; \quad f(x, y, z)=z \\ \iint_{\mathcal{S}} f(x, y, z) d S= \end{array} \]2 answers -
11. \( \iiint_{E} \frac{z}{x^{2}+z^{2}} d V \), where \[ E=\{(x, y, z) \mid 1 \leqslant y \leqslant 4, y \leqslant z \leqslant 4,0 \leqslant x \leqslant z\} \]2 answers -
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1,(a)(b)(c)
1. Evaluate the following double integral a. \( \int_{-2}^{2} \int_{0}^{2 x}\left(2 x \sin y-y^{2}\right) d y d x \) b. \( \int_{0}^{1} \int_{1}^{2 y-1}\left(3 x^{2} y+y^{2}\right) d x d y \) c. \( \i4 answers -
solve the system
\( y^{\prime}=\left(\begin{array}{lll}2 & 2 & 1 \\ 1 & 3 & 1 \\ 1 & 2 & 2\end{array}\right) y \)2 answers -
Solve the differential equation subject to the initial conditions. \[ \begin{array}{l} x \frac{d y}{d x}+y=\cos x ; x>0 ; x=\pi \text { when } y=1 \\ y=\frac{\sin x+\pi}{x}, x>0 \\ y=\frac{\sin x+\pi2 answers -
Solve the differential equation. \[ \begin{array}{r} e^{x} \frac{d y}{d x}+4 e^{x} y=3, x>0 \\ y=e^{-4 x}+c e^{-x}, x>0 \\ y=e^{-x}+e^{-4 x}, x>0 \\ y=e^{x}+c e^{-4 x}, x>0 \\ y=e^{-x}+c e^{-4 x}, x>02 answers