Calculus Archive: Questions from April 05, 2023
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Evaluate \( \iiint_{E} 3 x z d V \) where \( E=\{(x, y, z) \mid 2 \leq x \leq 5, x \leq y \leq 2 x, 0 \leq z \leq x+3 y\} \)2 answers -
Question 2 (a) Find \( y^{\prime} \) by implicit differentiation (i) \( \sqrt{x}+\sqrt{y}=1 \) (iii) \( \sin (x y)=\cos (x+y) \) (b) Find \( y^{\prime \prime} \) by implicit differentiation (i) \( x^{2 answers -
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Find the positive values of \( x \) and \( y \) that maximize \( Q=3 x y^{2} \) if \( 2 x+y=21 \) \[ \begin{array}{l} x=\frac{7}{2}, y=14 \\ x=5, y=11 \\ x=7, y=7 \\ x=2, y=17 \end{array} \] Find the2 answers -
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Which of the following is an implicit solution to the initial value problem \[ \begin{array}{l} \quad\left(e^{x} \sin y-2 y \cos x+x^{2}\right)+\left(e^{x} \cos y-2 \sin x+e^{y}\right) y^{\prime}=0, \2 answers -
Which of the following is an implicit solution to the initial value problem \[ \left(e^{x} \sin y-2 y \cos x+x^{2}\right)+\left(e^{x} \cos y-2 \sin x+e^{y}\right) y^{\prime}=0, \quad y(0)=0 \] \[ e^{x2 answers -
m \#1: Find the domain of the function \( f(x, y)=\ln \left(2 x^{2}+2 y+1\right) \) The set of all ordered pairs \( (x, y) \) for which: (A) \( y \geq \frac{1+2 x^{2}}{2} \) (B) \( y \geq-\frac{1+2 x^2 answers -
21 & 26 step by step
In Exercises 9-58, identify the coordinates of any local and absolute Graphing Functions extreme points and inflection points. Graph the function. 9. \( y=x^{2}-4 x+3 \) 10. \( y=6-2 x-x^{2} \) 11. \(2 answers -
Evaluate the integral \[ \iint_{R} 4 \arctan \left(\frac{y}{x}\right) d A \] here \( R=\left\{(x, y) \in \mathbb{R}^{2}: 0 \leq x^{2}+y^{2} \leq 1,0 \leq x \leq y\right\} \)2 answers -
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(1 point) Let \[ \int_{0}^{2} f(x) d x=-11, \quad \int_{0}^{3} f(x) d x=-12, \int_{0}^{2} g(x) d x=-6, \quad \int_{2}^{3} g(x) d x=-1, \] Use these values to evaluate the given definite integrals. a)2 answers -
Calculate a and b for vi - x
3. For the following vector fields, compute the following: (a) \( \nabla \times \vec{F} \) (b) \( \nabla \cdot \vec{F} \) (i) \( \langle y, 0\rangle \) (vii) \( \langle y, x\rangle \) (ii) \( \langle2 answers -
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Determine whether the vector field \( \vec{F} \) is conservative for all \( \mathbb{R}^{2} \) or \( \mathbb{R}^{3} \), unless otherwise indicated. If so, find a function \( f \) such that \( \vec{F}=\2 answers -
I. Halle el diferencial total a) \( z=e^{x} \operatorname{sen}(y) \) b) \( w=\frac{x+y}{z-3 y} \) II. Considere la función \( f(x, y)=y e^{x} \) y trabaje: a) Evaluar \( f(2,1) \) y \( f(2.1,1.05) \)2 answers -
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Problem 6.3 Find the GS of \[ y^{\prime \prime}+9 y=\tan (3 x) \] Problem 6.4 Find the GS of \[ y^{\prime \prime \prime}-y^{\prime \prime}+y^{\prime}-y=1+\sin x+\sin 2 x+e^{x}+e^{-x} \]2 answers -
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Given \( \vec{x}+\vec{y}=-\vec{\imath}+2 \vec{\jmath}+5 \vec{k} \) and \( \vec{x}-\vec{y}=3 \vec{\imath}+6 \vec{\jmath}-7 \vec{k} \), determine \( \vec{x} \) and \( \vec{y} \).2 answers -
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Evaluate the following integrals: 1. \( \iint_{R} \sin x \cos y d A \) where \( R=\left\{(x, y) \mid 0 \leq x \leq \frac{\pi}{3}, 0 \leq y \leq \frac{\pi}{4}\right\} \)2 answers -
Evaluate the double integral. \[ \iint_{D} 4 y \sqrt{x^{2}-y^{2}} d A, \quad D=\{(x, y) \mid 0 \leq x \leq 3,0 \leq y \leq x\} \]2 answers -
Honlema En una empresa, el costo total de la manufactura de una santidad de qunidades durante undia de produccjón, es daclo por: \( C(q)=0.2 q^{2}+q+900 \), dolames. Por experiencia, se ha determinac2 answers -
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\( \begin{array}{l}\int_{0}^{2} f(x, y) d x \text { and } \int_{0}^{3} f(x, y) d y \\ f(x, y)=9 x+3 x^{2} y^{2} \\ \int_{0}^{2} f(x, y) d x= \\ \int_{0}^{3} f(x, y) d y=\end{array} \)2 answers -
Find \( \int_{0}^{2} f(x, y) d x \) and \( \int_{0}^{3} f(x, y) d y \) \[ f(x, y)=11 y \sqrt{x+2} \] \[ \int_{0}^{2} f(x, y) d x= \] \[ \int_{0}^{3} f(x, y) d y= \]2 answers -
Let \( 7 \sin x+4 \cos y=3 \). \[ \begin{array}{l} \frac{d y}{d x}= \\ \frac{d^{2} y}{d x^{2}}= \end{array} \]2 answers -
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1. \( 4 x \cos y+6 \cos 2 y=5 \sin y \) 2. \( 4 x \sin y+6 \sin 2 y=5 \cos y \) 3. \( 4 x \sin y+6 \cos 2 y=5 \cos y \) 7. \( 4 x \cos y+6 \sin 2 y=5 \sin y \) \[ \begin{array}{l} y^{\prime}=\frac{4 \0 answers -
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Find \( y^{\prime} \) by implicit differentiation. Match the equations defining \( y \) implicitly with the letters labeling the expressions for \( y^{\prime} \). 1. \( 4 x \cos y+6 \cos 2 y=5 \sin y2 answers -
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Sea f(x,y) = e^(xy). Encuentra la ecuación del plano tangente a la gráfica de f en el punto (1,1).0 answers
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Encuentre el área de la superficie obtenida al rotar la curva y=1+2x^2 de x=0 a x=2 sobre el eje y.1 answer
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