Let w = x*y cos(2z). Find the following. (a) (x, y, z) : (b) (x, y, z) (c) x, y, z) az (d) (3, y, z) (e) (3,5, e) =( (f) (3,5,0) az

Q: Suppose f(x) = sin 4-x). Evaluate: x) dx (A - 3cos FC B -cos 3 X-4+ C 3 Cos 3 (D) 3cos -x- 4)+C

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Q: Let ro)-플-x a-글 FW) = b = 0, and n=3. Then: cos (f(x))dx =

A: We can find the integration as below

Q: Let w = x°y cos(4z). Find the following. a) (x, Y, z) = Əx b) (x, y, z) = dy c) dz (x, Y, z) · (d) -…

A: Topic = Derivative

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Q: (a) fr = 4xz2, fy = yz and f; = xz 2 sin (x), fy = cos(x)y and f: = e" z z + y? If, f = = frâ + fyŷ…

A: a) Given f=fx+fy+fz and F→=fx x^+fy y^+fz z^ and  fx=4xz2, fy=yz, fz=xz So, we have f=fx+fy+fz…

Q: 3. If G = (2x²y – x*)î + (e*y + y sin x)j+ (x² cos y)k, find: %3D дхду

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Q: f(r,t) = cos(3r) exp(4t) %3D fi(x,t)+ frz(x,t) = f(r,t) %3D

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Q: find ap for f(x) =cos 2 [0,2n]

A: a0=0

Q: Question 9: Calculate r (t). r (t) = (4t, 2e2t + 1, 2 sin(t)) ®F(t) = (4t, 2e2ª – 1,2 sin(t)) O F(t)…

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Q: Let g(8) = (2s – 1)°. Then g'(8) is 9'(1) is 9'"(8) is and g''(1) is

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Q: Given a function f(r, y, z) = cos (z + ry?z²), find: f-(,1,1) = f (T, 1, 1) = Your answers should be…

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Q: If y = 2 sin ( 3x+ n) –1 , The range is : (- 3,1) O (-1,3) O (-2,2) O (-3,3) O

A: the given function is  y = 2 sin3x+π-1

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A: Harmonic function: A two variable function ux, y is said to be harmonic, if the function is twice…

Q: c) If f(x, y)= e" cos 2x, then show that = 0.

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Q: Given f(x, y) = cos(5x + 2y), find faz(x, y) = -25 cos (5x + 2y) fay(x, y) = -cos (5x + 2y) fyy(x,…

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Q: For f(x1, x2) = x2 cos x1 find f'(x1, x2), f'(2,7) and df[(2,7); h]. For f(x, y, z) = (x – 2z)e"…

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Q: Suppose r' (t) = (cos(t), et, 2t) and r(0) = (1, 0, 3). Find r(t).

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Q: Question 8: The curve C in the ry-plane is parameterized by r (t). Find a parameterization of the…

A: Given:r→'t=4, 4e2t, 2costr→0=0,1,0

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A:

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Q: If f(x, y)= cos(x +y), then- (+: O a. - sin (x + y) O b. - cos(x+ y) COS O c. cos(x+ y) O d. sin (x…

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Q: Q3) for f(v) = sec2 (3v-1) and g(v) = tan2(3v- 1) show that %3D S(v) = g'(v).

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Q: BE F(t) = (cos(at), sin(at)) e G(t) = (eat, e-at), wiTH a > 0. CHECK IF a) F"(t) = -a²F(t)ANDf"(t) =…

A: Given F(t)=(Cos (at),sin(at)) and G(t)=(e^at,e^-at) Now we will check the given statements as shown…