Calculus Archive: Questions from November 14, 2022
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Evaluate \( \iiint_{B} f(x, y, z) d V \) for the specified function \( f \) and \( B \) : \[ f(x, y, z)=\frac{z}{x} \quad 3 \leq x \leq 27,0 \leq y \leq 5,0 \leq z \leq 6 \] \[ \iiint_{B} f(x, y, z) d2 answers -
help me solve a please!
Calculate \( \int_{C} \vec{F} \cdot d r \). (a) \( \vec{F}(x, y)=\langle-5,10\rangle, r(t)=\langle 3 \cos t, 3 \sin t\rangle, 0 \leq t \leq \frac{\pi}{2} \). (b) \( \vec{F}(x, y)=\left\langle-x^{2}, y2 answers -
help me solve b please!
Calculate \( \int_{C} \vec{F} \cdot d r \). (a) \( \vec{F}(x, y)=\langle-5,10\rangle, r(t)=\langle 3 \cos t, 3 \sin t\rangle, 0 \leq t \leq \frac{\pi}{2} \). (b) \( \vec{F}(x, y)=\left\langle-x^{2}, y2 answers -
help me solve c please!
Calculate \( \int_{C} \vec{F} \cdot d r \). (a) \( \vec{F}(x, y)=\langle-5,10\rangle, r(t)=\langle 3 \cos t, 3 \sin t\rangle, 0 \leq t \leq \frac{\pi}{2} \). (b) \( \vec{F}(x, y)=\left\langle-x^{2}, y2 answers -
help me solve d please!
Calculate \( \int_{C} \vec{F} \cdot d r \). (a) \( \vec{F}(x, y)=\langle-5,10\rangle, r(t)=\langle 3 \cos t, 3 \sin t\rangle, 0 \leq t \leq \frac{\pi}{2} \). (b) \( \vec{F}(x, y)=\left\langle-x^{2}, y2 answers -
help me solve e please!
Calculate \( \int_{C} \vec{F} \cdot d r \). (a) \( \vec{F}(x, y)=\langle-5,10\rangle, r(t)=\langle 3 \cos t, 3 \sin t\rangle, 0 \leq t \leq \frac{\pi}{2} \). (b) \( \vec{F}(x, y)=\left\langle-x^{2}, y2 answers -
2 answers
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\( 7,15,22,25 \) Find \( d y / d x \). 7. \( y=\ln \left(\frac{x}{1+x^{2}}\right) \) 15. \( y=x^{2} \log _{2}(3-2 x) \) 22. \( y=\ln (\cos x) \) 25. \( y=\log \left(\sin ^{2} x\right) \)4 answers -
If \( R=\{(x, y) \mid-1 \leq x \leq 2 \) and 1 \( \leq y \leq 6 \) evaluate \( \iint_{R}\left(x^{2} y+3 x^{2}\right) d A \)2 answers -
2. Use logarithmic differentiation to find \( y^{\prime} \). (a) \( y=x^{\cos x} \) (b) \( y=\frac{\sqrt{x+1}(2-x)^{5}}{(x+3)^{7}} \)2 answers -
Find all the first order partial derivatives for the following function. \[ \begin{aligned} f(x, y)=\sin ^{2}\left(4 x y^{2}-y\right) \\ f_{x}(x, y) &=2 \sin \left(4 x y^{2}-y\right) \cos \left(4 x y^2 answers -
please answer on a paper thank you
Question 7 (10 points). Find \( y^{\prime} \) and \( y^{\prime \prime} \) a) \( y=\ln \left(x+\sqrt{1+x^{2}}\right) \) b) \( y=\ln (\sec x+\tan x) \) c) \( y=\frac{\ln x}{x^{2}} \) d) \( y=e^{\ln \lef2 answers -
Maximize \( p=2 x+y \) subject to \[ \begin{array}{r} x+2 y \geq 14 \\ 2 x+y \leq 14 \\ x+y \leq 5 \end{array} \]2 answers -
The table below shows values for \( f(x, y)=\frac{3 x y}{x^{2}+3 y^{2}} \). Use the table to make a conjecture about the imit of \( f(x, y) \) as \( (x, y) \) approaches \( (0,0) \). If the limit does2 answers -
Find all solutions on the interval \( [0,2) \pi \) \[ \begin{array}{l} -\tan (x) \sin (x)-\sin (x)=0 \\ -\cos ^{\wedge} 2 x=1 / 2 \\ -\tan ^{\wedge} 5(x)-9 \tan (x)=0 \end{array} \]2 answers -
2 answers
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7. Determine \( \left.\frac{d y}{d x}\right|_{x=-2} \) if \( y=u^{3}-u \) and \( u=\sqrt[3]{3 x-2} \).2 answers -
7. Determine \( \left.\frac{d y}{d x}\right|_{x=-2} \) if \( y=u^{3}-u \) and \( u=\sqrt[3]{3 x-2} \).2 answers -
2 answers
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\( x=4 u+7 v-2 w, y=6 u+2 v-8 w \), and \( z=-(9 u+v+9 w) \) implies \( \frac{\partial(x, y, z)}{\partial(u, v, w)}= \)2 answers -
\( x=8 u v-6 u, y=7 u v w-4 u v \), and \( z=-6 u v w \) implies \( \frac{\partial(x, y, z)}{\partial(u, v, w)}= \)2 answers -
Sea Y(x) = A_{0} * x ^ 2 + A_{1}*x + A_{2} una solución para y^ prime prime + 4y = 4x ^ 2 donde \{A_{0}, A_{1}, A_{2}\} son números constantes. Entonces A_{2} =\
\( \operatorname{Sea} y(x)=A_{0} x^{2}+A_{1} x+A_{2} \) una solución para \( y^{\prime}+4 y=4 x^{2} \) donde \( \left[A_{0}, A_{1}, A_{2}\right] \) son números constantes. Entonees \( A_{2} \) : a)2 answers -
1. is convergent if d. none of the above
3. \( \int_{-1}^{3} \frac{1}{x} d x= \) a. 0 b. \( \ln 3 \) c. diverge d. ninguna de las anteriores 1. \( \sum_{n=1}^{\infty} a r^{n-1} \) es convergente si a. \( |r|1 \) d. ninguna de las anteriores2 answers -
Using the integral test, determine whether it converges or diverges. Verify that all conditions for applying this test are met
24. (10\%) Usando la prueba de la integral, determine si \( \sum_{n=2}^{\infty} \frac{\ln n}{n^{2}} \) converge o diverge. Verifique que todas las condiciones para aplicar esta prueba se cumplen:2 answers -
An example of a series ... convergent and limit .... is
17. Un ejemplo de una serie \( \sum a_{n} \) convergente y \( \lim a_{n} \neq 0 \) es0 answers -
21. calculate e length of curve of y 22.Calculate the surface area of revolution when rotating about the x-axis the graph of
21. (10\%) Calcule el largo de curva de \( y=\ln (\cos x), 0 \leq x \leq \frac{\pi}{3} \) 22. (10\%) Calcule el area de superficie de revolucion al rotar con respecto al eje de \( x \) la grafica de \2 answers -
please show the work
1. \( \sum_{n=1}^{\infty} a r^{n-1} \) es convergente si a. \( |r|1 \) d. ninguna de las anteriores 2. Si \( \sum_{n=1}^{\infty} a r^{n-1} \) es convergente, el valor seria a. \( \frac{a}{1-r} \) b. \2 answers -
please show the work
3. \( \int_{-1}^{3} \frac{1}{x} d x= \) a. 0 b. \( \ln 3 \) c. diverge d. ninguna de las anteriores2 answers -
2 answers
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please show the work
11. Una parametrizacion del circulo unitario es a. \( x=\cos t, y=\sin t, 0 \leq t \leq 2 \pi \) b. \( x=\sin t, y=\cos 2 t, 0 \leq t \leq 2 \pi \) c. \( x=\sin 2 t, y=\cos t, 0 \leq t \leq 2 \pi \) d2 answers -
Translation: 23-Find the equation of the tangent line to the curve parameterized by x=3cos(t) , y=sin(t) , at the point t=pi/4. 24-Using the integral test, determine if *excercise* converges or dive
23. (5\%) Halla la ecuacion de la recta tangente a la curva parametrizada por \( x=3 \cos t, y=\sin t \) en el punto \( t=\frac{\pi}{4} \) : 24. (10\%) Usando la prueba de la integral, determine si \(2 answers -
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27-28 Describe the domain of \( f \) in words. 28. (a) \( f(x, y)=\frac{\sqrt{4-x^{2}}}{y^{2}+3} \) (b) \( f(x, y)=\ln (y-2 x) \) (c) \( f(x, y, z)=\frac{x y z}{x+y+z} \)2 answers -
Translation: 21-Calculate the length of the curve y=ln(cos x) , 0<=x<=pi/3 22-Calculate the surface area of revolution as you rotate about the x-axis to the graph of y=sqrt(1+e^x) , 0<=x<
III. Conteste las siguientes preguntas \( (35 \%) \) 21. (10\%) Calcule el largo de curva de \( y=\ln (\cos x), 0 \leq x \leq \frac{\pi}{3} \). 22. (10\%) Calcule el area de superficie de revolucion a2 answers -
14. the integral is a. convergent b. improper type ii c.divergent d. None of the above 15. the integral is a. covergent b.improper to type ii c. a and b are correct d. None of t
14. La integral \( \int_{1}^{\infty} \frac{1}{x} d x \) es a. convergente b. impropia de tipo II c. divergente d. ninguna de las anteriores 15. La integral \( \int_{0}^{1} \frac{1}{x} d x \) es a. con2 answers -
Choose the right answer (Whole process is required, not just choosing the right one).
1. \( \sum_{n=1}^{\infty} a r^{n-1} \) es convergente si a. \( |r|1 \) d. ninguna de las anteriores 2. Si \( \sum_{n=1}^{\infty} a r^{n-1} \) es convergente, el valor seria a. \( \frac{a}{1-r} \) b. \2 answers -
d. none of the above
12. \( \lim _{n \rightarrow \infty} \frac{3-n-n^{2}}{n^{2}+2 n+1}= \) a. 0 b. 3 c. \( -1 \) d. ninguna de las anteriores 13. \( \sum_{n=1}^{\infty} 2^{n-1} 5^{1-n}= \) a. \( \infty \) b. 2 c. \( \frac2 answers -
Choose the right answer (both require full procedure, not just choosing the correct answer)
12. \( \lim _{n \rightarrow \infty} \frac{3-n-n^{2}}{n^{2}+2 n+1}= \) a. 0 b. 3 c. \( -1 \) d. ninguna de las anteriores 13. \( \sum_{n=1}^{\infty} 2^{n-1} 5^{1-n}= \) a. \( \infty \) b. 2 c. \( \frac2 answers -
11. A parameterization of the unit circle is d. all
10. La integral del largo de curva de \( y=\ln (\cos x), 0 \leq x \leq \frac{\pi}{3} \) es a. \( L=\int_{0}^{\pi / 3} 2 \pi \tan x d x \) b. \( L=\int_{0}^{\pi / 3} \sqrt{1+\sec ^{2} x} d x \) c. \( L2 answers -
d. none of the above
6. \( \lim _{n \rightarrow \infty} n \sin \left(\frac{1}{n}\right)= \) a. \( \pi \) b. 0 c. 1 d. ninguna de las anteriores 7. \( \lim _{n \rightarrow \infty} \tan \left(\frac{1}{n}\right)= \) a. 0 b.2 answers -
Find the integral. \[ \int 4(2 x+5)^{3} d x \] \[ \frac{3}{8}(2 x+5)^{4}+C \] \[ \frac{1}{2}(2 x+5)^{4}+C \] \[ \frac{1}{4}(2 x+5)^{4}+C \] \[ \frac{3}{4}(2 x+5)^{4}+C \]2 answers -
12. \( \lim _{n \rightarrow \infty} \frac{3-n-n^{2}}{n^{2}+2 n+1}= \) a. 0 b. 3 c. \( -1 \) d. ninguna de las anteriores2 answers -
3. Se quiere construir una caja sin tapa a partir de una hoja de cartón de \( 20 \times 10 \mathrm{~cm} \). Para ello, se corta un cuadrado de lado \( \mathrm{L} \) en cada esquina y se dobla la hoja2 answers -
2 answers
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Find the integral. \[ \begin{array}{l} \int(1-6 x) e^{3 x-9 x^{2}} d x \\ 3(1-6 x) e^{3 x-9 x^{2}}+C \\ \frac{1}{3}(1-6 x) e^{3 x-9 x^{2}}+C \\ \frac{1}{3} e^{3 x-9 x^{2}}+C \\ 3 e^{3 x-9 x^{2}}+C \en2 answers -
Consider the function \[ f(x, y, z)=3 x^{5} y^{2} z-3 x y^{5} z^{4} \] Find the following partial derivatives. \[ \begin{array}{l} \frac{\partial f}{\partial x}(x, y, z)= \\ \frac{\partial f}{\partial2 answers -
2 answers
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Find the first partial derivatives of the function. \[ g(x, y)=3 \ln (6 x+\ln y) \] \[ g_{x}(x, y)= \] \[ g_{y}(x, y)= \]2 answers -
Evaluate the double integral. \[ \iint_{D}(2 x+y) d A, \quad D=\{(x, y) \mid 1 \leq y \leq 5, y-4 \leq x \leq 4\} \]2 answers -
find y' and y" please write detailed calculations
\( y=\ln (\sec x+\tan x) \) \( y=\frac{\ln x}{x^{2}} \) \( y=e^{\ln \left(\ln \left(\ln \left(e^{x}\right)\right)\right)} \)2 answers -
2 answers
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Find \( \frac{d y}{d x} \) for \( y=\int_{0}^{e^{x^{2}}} \frac{2}{\sqrt{t}} d t \) \[ \frac{d y}{d x}= \]2 answers -
please help
Find the gradient vector field \( (\vec{F}(x, y, z)) \) of \( f(x, y, z)=y^{2} \sin (5 x z) \). \[ \vec{F}(x, y, z)= \]2 answers -
help
(1 point) Match each function with one of the graphs below. A 1. \( f(x, y)=y^{2}+1 \) 2. \( f(x, y)=1+2 x^{2}+2 y^{2} \) 3. \( f(x, y)=e^{-y} \) 4. \( f(x, y)=1+y \)2 answers -
Find the Jacobian of the transformation. \[ x=6 u+-v, y=-5 u+-5 v \] \[ \frac{\partial(x, y)}{\partial(u, v)}= \]2 answers -
Solve the following second order differential equations: 1. \( y^{\prime \prime}-3 y^{\prime}+2 y=e^{3 x}\left(-1+2 x+x^{2}\right) \) 2. \( y^{\prime \prime}-4 y^{\prime}+3 y=e^{3 x}\left(6+8 x+12 x^{2 answers