Evaluate the integral by choosing a convenient order of integration: « сos(хy) сos1"(тӕ) dA; R —D | 0, , x 10, 피 NOTE: Enter the exact answer. x cos(xy) cos"(Tx) dA = CoS

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Q: Find V· (V x F), if F(x, y, z) = 7e"*i+ 9xe"j – 8e"²k. V· (V × F) =

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Q: Find these derivatives

A: Our Aim is to find the derivative of the following functions given below:-(i) y=e2x cos (x)(ii) y=ln…

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Q: +4

A: To check the convergence of the given improper integral:∫-∞2dxx2+4

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Q: Evaluate the definite integral. (9ti + 3+j + Vik) dt 9ti + 3tj tk dt

A: Topic = Integration

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A: Let's find.

Q: 1. Determine whether the series is convergent or divergent. If it's n=l e"+1 convergent, find its…

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Q: n/2 c sine Evaluate the iterated integrals J. r cos e dr de 0. A 1/6 B 1/2 c) 6 D) 11/9

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Q: 1. dt 15. y= 17. y 0 tan 0 d0

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Q: Inx 6. lim,

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Q: Find f. (x+ 1) (b) f'(x) = f(1) = 5 3.

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Q: dy Solve the derivative dx for the function: x = e'sint ; y = etcost

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Q: If x + 1 f(x) then find the global minimum of f on the interval [1, c∞)

A: Given; f(x)=x^2+1/x

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Q: The graphs of the function f (r) = 7- a and g(a) = 3 are given below. %3D 10 8 f(x) = 7-x2 4- g(x) =…

A: topic- area bounded by curves

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A: Given :r(t)=6costi+6sintj

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Q: If x + 1 f(x) then find the global maximum of on the interval [1, c0) Write DNE if there is no…

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Q: Find V · (F × G), if F(x,y, z) = 3xi+j+7yk and G(x, y, z) = xi+ yj – zk. V• (F × G) =

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Q: A particle is moving with the given data. Find the position of the particle. a(t) = t - 8, s(0) = 4,…

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Q: Find V x (V × F) if F(x, y, z) = 8xyj+7xyz k. V × (V × F) =

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Q: Find V · (V × F) if F(x, y, z) = 4 sin xi + 8 cos(7x – 8y)j + zk. V: (V × F)

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Q: Sketch a single graph of a function f which satisfies all of the following sign charts for f, f',…

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Q: The population P (in thousands) of Tallahassee, Florida, from 2000 through 2018 can be modeled by P…

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Q: ||r(t) × r"(t)|| Use the formula k(t) to find k(t). 13 r(t) = t'i+ t3j K(t) =

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Q: lim (3x + 1) sin(2x) 4x2

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Q: п! n4 n=1

A: The given series is: ∑n=1∞n!n4 Let, an=n!n4; n≥1

Q: y+1 - Z 4. Find the distance between the lines = z and x = 3 %3D -2

A: topic- distance between lines

Q: r(4) (arcsin(t), arcos(1),0

A: Given: rt=arcsint, arccost, 0   As we know that; ddxarcsinx=11-x2ddxarccosx=-11-x2

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Q: 10 Find div F and curl F if F(x, y, z) = xz°i+ 5y"x²j+ 4z?yk. div F= curl F=

A: Solution:

Q: dx 2.

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Q: Use the gradient to find the directional derivetive of the function at Pin the drecton of v n(x, y)…

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Q: Calculate the following derivative. (Use symbolic notation and fractions where needed.) d (15 Vsin…

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Q: Inx Evaluate the limit using L'Hospital's rule: Lima0 cosh

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Q: The position vector r describes the path of an object moving in the xy-plane. Position Vector Point…

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Q: (d) Select the correct choice below and fill in the answer box within the choice. O A. lim f(x) = X…

A: Let's find.

Q: Find curl (3z i + 4x j + 9y k). curl (3z i + 4x j + 9y k) = ( i )i + ( i

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Q: H.W (5) Solve the following differential equations of (3x -6xy)dx+(-3x' -2y)dy 0

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Q: Find lim f(x) for the given piecewise function. x-4 2х + 5 if x 4 If the limit does not exist,…

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Q: tan(0)² cos(0) d0

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Q: Calculate y" (x) and y" (x). бх — 6 y(x) (Use symbolic notation and fractions where needed.) y"(x) =…

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