Calculus Archive: Questions from September 07, 2022
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2. [8 Points] Find the Derivative, \( y^{\prime} \) : (a) \( y=x^{3} e^{-1 / x} \) (b) \( y=\frac{e^{\sin ^{2} x}}{(1+\cos x)} \)1 answer -
evaluate the integral 22, 30
21. \( \int \tan ^{4} x \sec ^{6} x d x \) 22. \( \int_{0}^{\pi / 4} \sec ^{4} \theta \tan ^{4} \theta d \theta \) 23. \( \int_{0}^{\pi / 3} \tan ^{5} x \sec ^{4} x d x \) 24. \( \int \tan ^{5} x \sec1 answer -
3. [8 Points] Evaluate each Integral: (a) \( \int 4 e^{3 x} \sqrt{2+e^{3 x}} d x \) (b) \( \int_{\pi / 3}^{\pi / 2}(\sin 2 \theta) e^{3 \cos ^{2} \theta} d \theta \)1 answer -
Find \( y^{\prime} \) by implicit differentiation. Match the equations defining \( y \) implicitly with the letters labeling the expressions for \( y^{\prime} \). 1. \( 6 x \cos y+5 \sin 2 y=3 \sin y1 answer -
Find \( \lim _{x \rightarrow 0} f(x) \) if, for all \( x, 10 \cos (2 x) \leq f(x) \leq 7 x^{2}+10 \)1 answer -
TRANSFORMACIONES LINEALES Necesito ayuda en los 2 ejercicios, por favor y gracias.
En cada problema primero, encuentre la matriz de transformación asociada. Defina \( T: \mathbb{R}^{3} \) en \( \mathbb{R}^{4} \) por \( T\left(\begin{array}{l}x \\ y \\ z\end{array}\right)=\left(\beg0 answers -
Find the explicit solution of the differential equation \( \frac{y^{\prime}}{x^{2}+9}=\sqrt{1-y^{2}} ; y(0)=1 \). \[ \begin{array}{l} y=\sin \left(\frac{x^{3}}{3}+9 x+\frac{\pi}{2}\right) \\ y=\sin \l1 answer -
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2,6,10,12 please
11. \( \int_{0}^{\pi / 2} \sin ^{2} x \cos ^{2} x d x \) 12. \( \int_{0}^{\pi / 2}(2-\sin \theta)^{2} d \theta \) 1. \( \int \sin ^{3} x \cos ^{2} x d x \) 2. \( \int \cos ^{6} y \sin ^{3} y d y \) 131 answer -
Carlos decide montarle a una ventana regular de forma rectangular (ver figura) un semicirculo en el tope. Cuáles deben ser las dimensiones para la ventana que máximicen el área con un perímetro to
En la siguiente actividad usted resolverá el ejercicio que se presentan. La actividad tiene un valor de 12 puntos. Debe utilizar el procesador de palabras Microsoft Word \( (2010 \) o 2013), tipo de1 answer -
Find dy/dx show all steps for a,b,d,e
(a) \( y=e^{x \cos x} \) (b) \( y=x e^{2 x^{2}-4 x} \) (c) \( y=\ln \left(\sin \left(x^{2}\right)\right) \) (d) \( y=x \ln (4 x-3) \) (e) \( y=\ln \left(4-x^{3}\right) \) 5. Find \( \frac{d y}{d x} \)2 answers -
1) Compute the first partial derivatives \( f_{x}(x, y), f_{y}(x, y) \) of the following functions: (a) \( f(x, y)=3 x^{2} y-2 x y++7 y^{3}-4 x+3 \), (b) \( f(x, y)=\sin (3 x)+\cos (2 y)+\sin (x) \cos1 answer -
4) Compute all second partials, \( f_{x x}(x, y), f_{x y}(x, y), f_{y x}(x, y), f_{y y}(x, y) \), of the following functions without using Clairut's theorem: (a) \( f(x, y)=2 x^{3} y+4 x y^{2} \) (b)1 answer -
6) Compute \( f_{x}(x, y, z), f_{y}(x, y, z) \), and \( f_{z}(x, y, z) \) of the following functions: (a) \( f(x, y, z)=e^{x z}+\frac{x y}{z} \), (b) \( f(x, y, z)=x^{2} y z^{2}-4 \cos (y z) \), (c) \1 answer -
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Compute \( f_{x}(x, y, z), f_{y}(x, y, z) \), and \( f_{z}(x, y, z) \) of the following functions: (a) \( f(x, y, z)-e^{x z}+\frac{x y}{z} \), (b) \( f(x, y, z)-x^{2} y z^{2}-4 \cos (y z) \), (c) \( f1 answer -
1 answer
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7. Solve the following Second Order Non-Homogeneous Diffel \[ y^{\prime \prime}-y^{\prime}+\frac{1}{4} y=3+e^{x / 2} \]1 answer