Calculus Archive: Questions from July 10, 2023
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Sketch the graph of a twice-differentiable function \( y=f(x) \) with the properties given in the table. Choose the correct graph below.2 answers -
Solve the given DE using Laplace transforms 1. \( y^{\prime \prime}+5 y^{\prime}+4 y=5 e^{4 x}+4, y(0)=0, y^{\prime}(0)=1 \) 2. \( y^{\prime \prime}+9 y=2 x+1, y(0)=0, y^{\prime}(0)=1 \)2 answers -
The differential equation \[ (3 \tan (3 x)-3 \sin (3 x) \sin (y)) d x+(\cos (3 x) \cos (y)) d y=0 \] Has solutions of form \( F(x, y)=c \) where \[ F(x, y)= \]2 answers -
Determina el largo de arco de \( y=\frac{2}{3} x^{3 / 2}+3 \) en \( [3,6] \). \( L=\quad \) [Redondeado a la milésima]2 answers -
If \( \int_{0}^{8} f(x) d x=20 \) and \( \int_{0}^{8} g(x) d x=14 \), find \( \int_{0}^{8}[4 f(x)+5 g(x)] d x \). Answer:2 answers -
Expand the quotient by partial fractions. \[ \frac{y+4}{y^{2}(y+1)} \] A. \( -\frac{3}{y}+\frac{4}{y^{2}}+\frac{4}{y+1} \) B. \( \frac{4}{y^{2}}+\frac{3}{y+1} \) C. \( -\frac{3}{y}+\frac{4}{y^{2}}+\fr2 answers -
d) Compute \( \int \sin ^{2} x \cos ^{2} x d x \). e) Compute \( \int \sin ^{-3} x \cos x d x \). Compute the following: a) \( \int \tan x \sec ^{2} x d x \)2 answers -
La siguiente representa el volumen de un sólido: \[ \pi \int_{2}^{4} y^{4} d y \] Dibuje la gráfica utilizando un graficador en linea y describa el solido. Puede utilizar el siguiente enlace: hittp:2 answers -
Given \( f(x, y)=4 x^{8} \cos \left(y^{7}\right) \) \[ \begin{array}{l} f_{x y}(x, y)=\mid \\ f_{y y}(x, y)= \end{array} \]2 answers -
Región entre las curvas \( y=7 x+-12, y=x^{2} \) para \( 3 \leq x \leq 4 \). Determina el momento en \( y \). \[ M_{y}=\quad \text { [Fracción simplificada] } \] Determina el momento en \( x \). \[2 answers -
30 & 31 please
\( \begin{array}{l}\iint_{R} \frac{\tan \theta}{\sqrt{1-t^{2}}} d A, \quad R=\{(\theta, t) \mid 0 \leqslant \theta \leqslant \pi / 3, \\ \iint_{R} x \sin (x+y) d A, \quad R=[0, \pi / 6] \times[0, \pi2 answers -
Calcule los valores máximo y mínimo locales, y punto o puntos sillas de la función. \[ f(x, y)=x^{3}+y^{3}+3 x^{2}-3 y^{2}-8 \]2 answers -
Calcule la derivada direccional de la función en el punto dado en la dirección del vector \( u \). \[ \begin{array}{l} h(x, y, z)=\cos x y+e^{y z}+\ln z x, \quad P_{0}(1,0,1 / 2) \\ \mathbf{u}=\math2 answers -
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