Calculus Archive: Questions from November 26, 2022
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Solve the DE: y" + 4y = 2 when x = 0, y = 0 and when y = 1/2, x = pi/4.
Solve the DE: \( y^{\prime \prime}+4 y=2 \) when \( x=0, y=0 \) and when \( y=1 / 2, x=p i / 4 \). \[ \begin{array}{l} y=(\sin 2 x)^{\wedge} 2 \\ y=(\sin x)^{\wedge} 2 \\ y=\sin 2 x+1 / 2 \\ y=\cos 22 answers -
Evaluate the triple integral \( \iiint_{Q} f(x, y, z) d V \). \[ \begin{array}{l} f(x, y, z)=8 x+9 y-10 z, Q=\{(x, y, z) \mid 0 \leq x \leq 2,-6 \leq y \leq 6,1 \leq z \leq 6\} \\ \iiint_{Q} f(x, y, z2 answers -
2. \( (8 \mathrm{pts}) \) Find the gradient field of \( f \) if \( f(x, y, z)=x \sin \left(\frac{y}{z}\right) \).2 answers -
3. (12 pts) Let \( \mathbf{F}(x, y, z)=e^{x} \mathbf{i}+e^{x y} \mathbf{j}+e^{x y z} \mathbf{k} \). \[ e^{x+y e^{x y}+z e^{\text {(a) Find div }} \text { F } z} \] (b) Find \( \operatorname{curl} \mat2 answers -
2 answers
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Evaluar las siguientes integrales
Evaluar las siguientes integrales: 1. \( \int \ln x^{3} d x \) 2. \( \int\left(t^{3}-2 t^{2}+4 t-3\right) e^{2 t} d t \) 3. \( \int \sin ^{3} x \cos ^{2} x d x \) 4. \( \int \sec ^{3} \frac{x}{2} \tan2 answers -
1.find r'(t) for the condition 2. find r"(t) for the fuction
1. Halle \( r(t) \) para la siguiente condición \( r^{\prime}(t)=4 e^{2 t} i+3 e^{t} j, r(0)=2 i \) 2. Halle \( r^{\prime \prime}(t) \) de la siguiente función \( r(t)=4 \cos t i+4 \sin t j \)2 answers -
Evaluate the triple integral \( \iiint_{Q} f(x, y, z) d V \). \[ \begin{array}{l} f(x, y, z)=7 x+9 y-8 z, Q=\{(x, y, z) \mid 0 \leq x \leq 2,-5 \leq y \leq 5,0 \leq z \leq 4\} \\ \iiint_{Q} f(x, y, z)2 answers -
Evaluate the triple integral \( \iiint_{Q} f(x, y, z) d V \) \[ \begin{array}{l} f(x, y, z)=x^{2}+y^{4} \\ Q=\{(x, y, z) \mid 0 \leq x \leq 2,-2 \leq y \leq 2,0 \leq z \leq 1\} \end{array} \] A. \( \f2 answers -
If \( R=\{(x, y) \mid 0 \leq x \leq 2 \) and \( 1 \leq y \leq 4\} \), evaluate \[ \int_{R} \int\left(9 x^{2}+3 x y^{3}\right) d A \] The value is2 answers -
47. Examine the following functions for continuity: (a) \[ f(x, y)=\left\{\begin{array}{ll} \frac{x^{3} y}{x^{6}+y^{2}} & (x, y) \neq(0,0) \\ 0 & (x, y)=(0,0) \end{array}\right. \] (b) \[ g(x, y)=\lef2 answers -
Evaluate the triple integral \( \iiint_{Q} f(x, y, z) d V \) \[ \begin{array}{l} f(x, y, z)=x^{2}+y^{4} \\ Q=\{(x, y, z) \mid 0 \leq x \leq 2,-2 \leq y \leq 2,0 \leq z \leq 1\} \end{array} \] A. \( \f2 answers -
use the Winplot program and draw the graph f(x) 1/(x^2-2x-3) to tell whether the integral 0 to 2 f(x)dx is positive or negative. use the graph to give an estimate of the value of the integral, and the
Use el programa Winplot y dibuje la gráfica de \( f(x)=\frac{1}{\left(x^{2}-2 x-3\right)} \) para decidir si \( \int_{0}^{2} f(x) d x \) es positiva o negativa. Use la gráfica para dar una estimaci2 answers -
Consider the function \( \mathrm{F} \) of two variables: \( F(x, y)=f(g(x, y), h(x, y)) \) where \( f(s, t)=2 s^{2} t^{2}, g(x, y)=x^{2}+2 y, h(x, y)=x^{2} y^{2} \). Use the chain rule to find \( F_{x2 answers -
Question: 45,47,49,51,55
45-56 Use logarithmic differentiation to find the derivative of the function. 45. \( y=\left(x^{2}+2\right)^{2}\left(x^{4}+4\right)^{4} \) 46. \( y=\frac{e^{-x} \cos ^{2} x}{x^{2}+x+1} \) 47. \( y=\sq1 answer -
2 answers
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Please answer question 11,15
9-20 Find the exact length of the curve. 9. \( y=1+6 x^{3 / 2}, \quad 0 \leqslant x \leqslant 1 \) 10. \( 36 y^{2}=\left(x^{2}-4\right)^{3}, \quad 2 \leqslant x \leqslant 3, \quad y \geqslant \) 11. \2 answers -
\( \int \frac{\sec ^{2} x}{\left(4-\tan ^{2} x\right)^{3 / 2}} d x \) \( \frac{1}{4} \cot \theta+C \) \( \frac{-\tan x}{4 \sqrt{4-\tan ^{2} x}}+C \) \( \frac{\tan x}{4 \sqrt{4-\tan ^{2} x}}+C \) \( \f2 answers -
27 and 29
19-34 Sketch the region enclosed by the given curves and find its area. 19. \( y=12-x^{2}, \quad y=x^{2}-6 \) 20. \( y=x^{2}, \quad y=4 x-x^{2} \) 21. \( x=2 y^{2}, \quad x=4+y^{2} \) 22. \( y=\sqrt{x2 answers -
Halle el vector normal unitario para: a. \( r(t)=t \boldsymbol{i}+\frac{1}{2} t^{2} \boldsymbol{j} \), en \( t=2 \) b. \( r(t)=\pi \cos t \boldsymbol{i}+\pi \sin t \boldsymbol{j} \), en \( t=\frac{\pi2 answers -
En los siguientes ejercicios halle la longitud de arco en el intervalo dado: a. \( r(t)=t i+3 t j, \quad[0,4] \) b. \( r(t)=t^{3} \boldsymbol{i}+t^{2} \boldsymbol{j} \), \( \quad[0,2] \) c. \( r(t)=a2 answers -
2. En los siguientes ejercicios hallar la curvatura \( K \) de cada una: a. \( r(t)=t \boldsymbol{i}+t^{2} \boldsymbol{j}+\frac{t^{2}}{2} \boldsymbol{k} \) b. \( r(t)=2 t^{2} \boldsymbol{i}+t \boldsym2 answers -
I need help finding the limit for each of these problems.
2. Emaurthred linnite de las furrions dadas. a) \( \frac{\sqrt{2 x+3}-x}{x-3} \) b) \( \frac{\sqrt{5+x}-\sqrt{5}}{\sqrt{2 x}} \) c) \( \frac{(2 x+1)(x-1)}{2 x-1} \)0 answers -
1. Sketch the following vector fields (a) \( \mathbf{F}(x, y)=2 \mathbf{i}+y^{2} \mathbf{j} \) (b) \( \mathbf{F}(x, y)=\nabla f \) where \( f(x, y)=4 x^{2}+y^{2} \)2 answers -
2 answers
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Evaluate the integral. ∫07∫−49−x249−x2∫−49−x2−z249−x2−z21(x2+y2+z2)1/2dydzdx =
Evaluate the integral. \[ \int_{0}^{7} \int_{-\sqrt{49-x^{2}}}^{\sqrt{49-x^{2}}} \int_{-\sqrt{49-x^{2}-z^{2}}}^{\sqrt{49-x^{2}-z^{2}}} \frac{1}{\left(x^{2}+y^{2}+z^{2}\right)^{1 / 2}} d y d z d x= \]2 answers -
1.In the following exercises, find the arc length in the given interval: 2. In the following exercises, find the curvature K of each one: need all amswers please 😭🙏🏻
1. En los siguientes ejercicios halle la longitud de arco en el intervalo dado: a. \( r(t)=t i+3 t \boldsymbol{j}, \quad[0,4] \) b. \( r(t)=t^{3} \boldsymbol{i}+t^{2} \) j, \( \quad[0,2] \) c. \( r(t)2 answers -
2 answers
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2 answers
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If \( x=1+2 \tan t \) and \( y=2+\sec t \), find \( d^{2} y / d x^{2} \) \[ \begin{array}{l} \frac{\sin t}{2} \\ \frac{\cos ^{3} t}{2} \\ \frac{\sin ^{3} t}{2} \\ \frac{\cos ^{2} t}{2} \end{array} \]2 answers