Calculus Archive: Questions from November 29, 2022
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Find the differential (total) of the following functions. Simplify your response
3. Halle la diferencial (total) de las siguientes funciones. Simplifique su respuesta a. \( \mathrm{Z}=e^{-2 x} \cos 2 \pi t \) b. \( \mathrm{z}=\sqrt{x^{2}+3 y^{2}}= \)2 answers -
Find the differential (total) of the following functions. Simplify your response a)find using chain ruel b)fin dz/ds if s=1
4. Si \( \mathbf{z}=\sqrt{2 y-x}, x=e^{s}-1, y=\ln (x s+s) \) a. Halle \( \frac{d z}{d s} \) utilizando la regla de la cadena b. Halle el valor de \( \frac{d z}{d s} \) si s \( =1 \)2 answers -
2 answers
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If \( f(x, y)=\frac{x^{2} y}{\left(3 x-y^{2}\right)} \), find the following (a) \( f(1,4) \) (b) \( f(-3,-1) \) (c) \( f(x+h, y) \) (d) \( f(x, x) \)2 answers -
Regards
Find the furst denvative of \( \begin{array}{ll}\text { a. } y=\frac{1}{(2 x+3)^{2}} & \text { (b) } y=\frac{4}{\sqrt{x}}\end{array} \) c \( f(x)=\frac{3 x-1}{2 x+5} \quad \) (d) \( y=\frac{\sin x+\co2 answers -
5 cosxdz+(1+2/y) sen x dy ,6(y*2+xy*3)dx+(5y*2-xy+y*3seny)dy= 0 convet to lineal
\( \cos x d x+\left(1+\frac{2}{y}\right) \operatorname{sen} x d y \) \( \left(y^{2}+x y^{3}\right) d x+\left(5 y^{2}-x y+y^{3} \operatorname{sen} y\right) d y=0 \)2 answers -
3. Para \( \phi(x, y, z)=3 x^{2} y-y^{2} z^{2} \). Encuentre \( \nabla \phi(\circ \) grad \( \phi) \) en el punto \( (1,-2,-1) \).2 answers -
Determine la constante \( a \) de modo que el vector siguiente sea solenoidal. \[ \mathbf{V}=(-4 x-6 y+3 z) \mathbf{i}+(-2 x+y-5 z) \mathbf{j}+(5 x+6 y+a z) \mathbf{1} \] Un vector \( \mathbf{V} \) es2 answers -
2 answers
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2. Express the following integral in cylindrical coordinates \[ \int_{0}^{2} \int_{0}^{\sqrt{2 x-x^{2}}} \int_{0}^{\sqrt{x^{2}+y^{2}}} f(x, y, z) d z d y d x \]2 answers -
12. For the región evaluate \[ R=\{(x, y) \mid 0 \leq x \leq 2,1 \leq y \leq 4\} \quad \iint\left(6 x^{2}+4 x y^{3}\right) d A \]2 answers -
4. Find the derivative. (a) \( y=(\sec x \tan x)^{\cos x}+\frac{1}{4^{\sin x^{3}}} \) (b) \( y=\frac{\sqrt{x^{2}+1} \tan ^{-1} x}{\left(1+\sqrt{e^{x}}\right) \log x^{2}} \) (c) \( y=\sin ^{-1}(\cos x)2 answers -
2 answers
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\( f(x, y)=\sqrt{4-4 x^{2}-y^{2}} \) \( f(x, y)=y^{2}+1 \) \( f(x, y)=1+2 x^{2}+2 y^{2} \) \( f(x, y)=1+y \)2 answers -
Calculate all four second-order partial derivatives of \( f(x, y)=\sin \left(\frac{2 x}{y}\right) \). \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y)= \] \[ f_{y x}(x, y)= \] \[ f_{y y}(x, y)= \]2 answers -
(5pts) Suppose that \( \gamma^{\prime \prime}(t)=e^{5 t} \mathbf{i}+\cos (3 t) \mathbf{j}+t^{2} \mathbf{k}, \gamma(0)=\mathbf{i}+2 \mathbf{j}+3 \mathbf{k}, \gamma^{\prime}(0)=-2 \mathbf{i}+\mathbf{j}+2 answers -
2 answers
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0 answers
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The Quotient Rule. i) \( y=\frac{10 x^{8}-6 x^{7}}{2 x} \) (Ans. \( \left.\frac{d y}{d x}=35 x^{6}-18 x^{5}\right) \), ii) \( y=\frac{3 x^{8}-4 x^{7}}{4 x^{3}} \) (Ans. \( \frac{d y}{d x}=\frac{15}{4}2 answers -
2 answers
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Please show all work, thumbs up!
\( y^{\prime} \) if \( y=\left(2 x^{3}-5 x\right) \ln (4 \) \( y^{\prime} \) if \( y=\left(x^{3}+2 x\right) e^{-5 x} \)2 answers -
Please show all work, thumbs up!
\( y^{\prime} \) if \( y=\frac{x^{3}}{e^{2 x}} \) \( y^{\prime} \) if \( y=\ln e^{\left(x^{2}+3 x\right)} \)2 answers -
Please show all work, thumbs up!
ad \( y^{\prime} \) if \( y=e^{-4 x} \ln 5 \) ad \( y^{\prime} \) if \( y=x^{\left(x^{2}+3 x\right)} \)2 answers -
2 answers
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Calcule el volumen contenido entre las rectas \[ \begin{array}{l} x=0, \quad x=0.5 \\ y \text { la función } \\ f(x)=\left(1-x^{2}\right) \end{array} \]2 answers -
Which of the following series is condicionally convergent (show full procedure, not just selecting the right answer):
3. La siguiente serie es condicionalmente convergente: a. \( \sum_{n=1}^{\infty} \frac{(-1)^{n}}{n} \) b. \( \sum_{n=1}^{\infty} \frac{(-1)^{n}}{n^{2}} \) c. \( \sum_{n=1}^{\infty} n \) d. ninguna de2 answers -
2 answers
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Find the derivative. 4) \( y=8 e^{-4} x \) A) \( 8 x e^{-32 x} \) B) \( -32 x e^{-4 x} \) C) \( 8 e^{-32 x} \) D) \( -32 e^{-4 x} \)2 answers -
Find the derivative of the function.
\[ y=\frac{x^{2}+8 x+3}{\sqrt{x}} \] A) \( y^{\prime}=\frac{2 x+8}{x} \) B) \( y^{\prime}=\frac{3 x^{2}+8 x-3}{x} \) C) \( y^{\prime}=\frac{3 x^{2}+8 x-3}{2 x^{3 / 2}} \) D) \( y^{\prime}=\frac{2 x+8}2 answers -
2 answers
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Find the derivative of the function. 11) \( y=\sqrt{4 x+2} \) A) \( y^{\prime}=\frac{4}{\sqrt{4 x+2}} \) B) \( y^{\prime}=\frac{8}{\sqrt{4 x+2}} \) C) \( y^{\prime}=\frac{1}{\sqrt{4 x+2}} \) D) \( y^{2 answers -
Calculate the volume contained between the lines. x=0, x=0.5 and the function f(x)=(1-x^2)
Calcule el volumen contenido entre las rectas \[ x=0, \quad x=0.5 \] y la función \[ f(x)=\left(1-x^{2}\right) \]2 answers -
pls help me find derivate and show work
(e) \( y=q^{3}-3 \ln (q) \) (f) \( y=\left(t^{2}-8 t\right) e^{3 t} \) (g) \( y=\frac{1+3 z+z^{2}}{\ln (z)} \) (h) \( f(t)=\ln \left(3^{t}-t^{2}+1\right) \) (i) \( y=\ln (\ln (x)) \) (j) \( P=(1+\ln (2 answers -
2 answers
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Find the values of the function. \[ g(x, y)=x^{2} e^{5 y} \] (a) \( g(-5,0) \) (b) \( g\left(5, \frac{1}{5}\right) \) (c) \( g(1,-1) \) (d) \( g(-6, y) \)2 answers -
answer now
4. Suponga que \( g(t)= \) es el vector posición de una partícula en movimiento, donde \( t \) representa el tiempo. En que momento la partícula pasa por el plano \( X Y \) ?, Cuál o cuáles son s0 answers -
Halle el arrea sombreada: Selected Answer: a. \( 7 / 3 \) Answers: a. \( 7 / 3 \) b. \( 5 / 3 \) c. \( 8 / 3 \) d. \( 6 / 3 \)2 answers -
Find the first partial derivatives of the function. \[ \begin{array}{c} f(x, y, z)=\frac{8 x}{y+z} \\ f_{x}(x, y, z)= \\ f_{y}(x, y, z)= \\ f_{z}(x, y, z)= \end{array} \]2 answers -
Find the first partial derivatives of the function \[ \begin{array}{l} f(x, y, z, t)=x y^{2} z^{6} t^{9} \\ f_{x}(x, y, z, t)= \\ f_{y}(x, y, z, t)= \\ f_{z}(x, y, z, t)= \\ f_{t}(x, y, z, t)= \end{ar2 answers -
Find all the second partial derivatives. \[ \begin{array}{l} f(x, y)=x^{6} y^{4}+5 x^{4} y \\ f_{x x}(x, y)=30 x^{4} y^{4}+60 x^{2} y \\ f_{x y}(x, y)= \\ f_{y x}(x, y)= \\ f_{y y}(x, y)= \end{array}2 answers -
5. Determine las derivadas parciales indicadas: (a) \( f(x, y)=x^{4} y^{2}-x^{3} y, f_{x x x}, f_{x y x} \) (b) \( f(x, y)=\operatorname{sen}(2 x+5 y), f_{y x y} \)2 answers -
Use la regla de la cadena para determinar \( \frac{d z}{d t} \). (a) \( z=x y^{3}-x^{2} y, x=t^{2}+1, y=t^{2}-1 \). (b) \( z=\operatorname{sen} x \cos y, x=\sqrt{t}, y=\frac{1}{t} \)2 answers -
Use regla de la cadena para determinar \( \frac{\partial z}{\partial s} \) y \( \frac{\partial z}{\partial t} \). (a) \( z=(x-y)^{5}, x=s^{2} t, y=s t^{2} \). (b) \( z=e^{r} \cos \theta, r=s t, \theta2 answers -
8. Use la regla de la cadena para determinar las derivadas parciales indicadas (a) \( z=x^{2}+x y^{3}, x=u v^{2}+w^{3}, y=u+v e^{w} \); \( \frac{\partial z}{\partial u}, \frac{\partial z}{\partial v},2 answers -
(c) If \( H(x, y, z)=x y z \vec{i}+\sin (x y) \vec{j}-\cos (y z) \vec{k} \), compute \( \nabla \times H(x, y, z) \).2 answers -
8. If \( y=\frac{1}{\sin x} \), find \( y^{\prime \prime} \) at \( x=\frac{\pi}{2} \). a. 1 c. 0 b. \( -1 \) d. \( \sqrt{2} \)2 answers -
URGENT answers only please
4. If \( f(x)=\cos (\sin x) \), find \( f^{\prime}(1) \). a. \( 0.2314 \) c. 0 b. 1 d. \( -0.4029 \) 5. If \( y=2 \sin x-\cos x \), find \( y^{\prime \prime} \) at \( x=\frac{\pi}{3} \). a. \( \frac{12 answers -
13. If \( f(x)=\sin ^{3} 2 x+x^{2} \), find \( f^{\prime \prime}\left(\frac{\pi}{4}\right) \). a. \( -10 \) b. 6 c. 10 d. 12 14. If \( f(x)=(2 \sin x \cos x)^{2}+3 x \), find \( f^{\prime \prime}\left2 answers -
find a function g such that...
3. Hallar una función \( g \) tal que: \( g^{\prime}(t)=6 i+6 t j+\left(3 t^{2}-t\right) k \), donde \( g(0)=i-2 j+k \)2 answers -
Find the equation of the tangent line to the curve given by: at t=1
2. Encuentre la ecuación de la recta tangente a la curva dada por: \[ f(t)=\text {, en } t=1 \]2 answers -
1. Calcula la longitud de la curva dada por \( y=\sqrt{4(x+4)^{3}} \), en \( 0 \leq x \leq 2 \). 2. Determina el área bajo la curva \( \frac{2 x^{4}-1}{x^{2}(x+1)^{2}} \), el eje \( x, y \mathrm{x}=40 answers -
2 answers
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4. If \( f(x)=\cos (\sin x) \), find \( f^{\prime}(1) \). a. \( 0.2314 \) b. 1 c. 0 d. \( -0.4029 \) 5. If \( y=2 \sin x-\cos x \), find \( y^{\prime \prime} \) at \( x=\frac{\pi}{3} \). a. \( \frac{12 answers -
Solve the ODE \[ y^{\prime \prime}-2 y^{\prime}=x+3 \] given \( y(0)=0 \) and \( y^{\prime}(0)=-\frac{15}{4} \) \[ y(x)= \]2 answers -
If \( y=\tan x \), find \( y^{\prime \prime} \) at \( x=\frac{\pi}{2} \). a. \( \frac{\sqrt{3}}{8} \) c. \( \frac{1}{2} \) b. \( 8 \sqrt{3} \) d. 12 answers -
help urgent
7. If \( y=\tan 2 x \), find \( y^{\prime \prime} \) at \( x=\frac{\pi}{2} \). a. \( \frac{\sqrt{3}}{8} \) c. \( -8 \) b. \( 8 \sqrt{3} \) d. 0 8. If \( y=\frac{1}{\sin x} \), find \( y^{\prime \prime2 answers -
7. If \( y=\tan 2 x \), find \( y^{\prime \prime} \) at \( x=\frac{\pi}{2} \). a. \( \frac{\sqrt{3}}{8} \) c. \( -8 \) b. \( 8 \sqrt{3} \) d. 02 answers -
8. If \( y=\frac{1}{\sin x} \), find \( y^{\prime \prime} \) at \( x=\frac{\pi}{2} \). a. 1 c. 0 b. \( -1 \) d. \( \sqrt{2} \)2 answers -
2 answers
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Encuentre el área acotada (limitada) por las funciones: 1) \[ f(x)=\sqrt{10-4 x^{2}} \] 2) \[ g(x)=0 \]2 answers -
3. If \( f(x)=\cos ^{2}(x) \), find \( f^{\prime}\left(\frac{\pi}{4}\right) \). a. 1 c. \( \frac{1}{2} \) b. \( -1 \) d. \( \frac{2}{\sqrt{2}} \)2 answers -
Help
Calculate \( \iint_{S} f(x, y, z) d S \) For \[ y=1-z^{2}, \quad 0 \leq x \leq 7, \quad 0 \leq z \leq 7 ; \quad f(x, y, z)=z \] \( \iint_{S} f(x, y, z) d S= \)2 answers -
suppose it converges a. Find lim, then test for sufficiently large values of n
22. Suponga que \( \sum_{n=1}^{\infty} a_{n} 3^{n} \) converge. a. (8\%) Encuentre \( \lim _{n \rightarrow \infty}\left(a_{n} 3^{n}\right) \). Luego pruebe que \( \sqrt[n]{a_{n}} \leq \frac{1}{3} \) p2 answers -
Which of the following numbers can be the radius of convergence of anx^n given that an3^n is convergent. justify answer
b. \( (7 \%) \) ¿Cual de los siguientes números puede ser el radio de convergencia de \( \sum_{n=1}^{\infty} a_{n} x^{n} \) dado que \( \sum_{n=1}^{\infty} a_{n} 3^{n} \) es convergente? Justifique2 answers -
Find the point on the plane Particularly Close to the origin. [Suggestion: Consider the square of The distance.]
23. Encuentre el punto sobre el plano \( x+2 y+z=1 \) más cercano al origen. [Sugerencia: Considere el cuadrado de la distancia.]2 answers -
19. the interval of convergence of is 20. the convergence of is
19. El intervalo de convergencia de \( \sum_{n=0}^{\infty} \frac{(x-1)^{n}}{2^{n}} \) es 20. La convergencia de \( \sum_{n=1}^{\infty}(-1)^{n}\left(\frac{n}{2 n-1}\right)^{n} \) es2 answers -
Find all the points on the surface Which are the closest to the origin. Determine the minimum distance
25. Encuentre todos los puntos sobre la superficie \( x y z=8 \) que son los más cercanos al origen. Determine la distancia mínima.2 answers -
is divergent if anwsers: c. a and b are correct d. none of the above
7. \( \sum_{n=1}^{\infty} \frac{1}{n^{p}} \) es divergente si a. \( p \leq 1 \) b. \( p>1 \) c. la a. y la b. son correctas d. ninguna de las anteriores2 answers -
3. conditionally convergent serie? 4. absolutely convergent serie? the answer D is: none of the above
3. La siguiente serie es condicionalmente convergente: a. \( \sum_{n=1}^{\infty} \frac{(-1)^{n}}{n} \) b. \( \sum_{n=1}^{\infty} \frac{(-1)^{n}}{n^{2}} \) c. \( \sum_{n=1}^{\infty} n \) d. ninguna de2 answers -
16. The proof of reason allows us to conclude that 17. The graph of is
16. La prueba de la razon para \( \sum_{n=1}^{\infty} \frac{1}{n^{1.1}} \) nos permite concluir que 17. La grafica de \( \left\{(x, y, z): 1 \leq x^{2}+y^{2}+z^{2} \leq 4, z \leq 0\right\} \) es2 answers -
2 answers
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2 answers
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Let \( F(x, y, z)=\left(6 x z^{2},-9 x y z, 3 x y^{3} z\right) \) be a vector field and \( f(x, y, z)=x^{3} y^{2} z \). \[ \begin{array}{l} \nabla f=(\text {, } \\ \nabla \times F=(\quad, \quad) \text2 answers -
2 answers
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2 answers
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Find the partial derivatives \( f_{x} \) and \( f_{y} \) if \( f(x, y)=10 x^{2} y^{3}+8 x y^{2}-3 x^{2} \). \[ f_{x}(x, y)= \] \[ f_{y}(x, y)= \]2 answers -
2 answers
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2. the interval of convergence of __ is
2. El intervalo de convergencia de \( \sum_{n=1}^{\infty} \frac{x^{n}}{2^{n-1}} \) es: a. \( [-1 / 2,1 / 2] \) b. \( (-1 / 2,1 / 2) \) c. \( (-1 / 2,1 / 2] \) d. ninguna de las anteriores 3. La siguie2 answers -
2 answers