Find the divergence of U = r cos 0 a, - sin 0 ag + 2r² sin 0 2 sin 0 3 sin 0 - r2 2 cos 0 3 cos 0 r2 2 cos 0 3 cos 0 - r 3 cos(03r2) 2 cos 0 r2 r2

Q: Let f (x) = f₁²² sin² (t)dt. Find ƒ' (π). ○ 2π sin² (π) π sin² (7²) ○ sin² (²) ○ 2π sin² (²)

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Q: X = cos 2t, y = cos t, 0 <t< n

A: given x=cos2t and y=cost interval 0&lt;t&lt;π  dx/dt =d/dt(cos2t) dx/dt=-2sin2t And dy/dt=d/dt(cost)…

Q: What is the dy/dx of y = 3sin²x cos x ? O 3 sin x(sin²x - 2cos²x) O-3 sin x(sin²x - 2cos²x) O 3 sin…

A: Given: y=3sin2⁡xcos⁡x To find: dydx We know that ddxcosx = -sinx ; ddxsinx = cosx

Q: Find the derivative. 26) dx 16t7 dt A) B) 2x5 - 2 C) 16x7/2 D) 8x3 sin t 1 27) du 25 - u2 1 - Cos t…

A: 26) To find the derivative  ddx∫1x16t7dt First find the integral ∫1x16t7dt=16∫1xt7dt…

Q: sin adx =? O A. - cos r + 2 Cos cos z | +e 4. O B.-z+2-증 O C. - cos x +2 cos I +C COS D. cos x cos 2…

A: Given: I=∫sin5xdx We know that sin2x=1-cos2x                                              ..1 So, by…

Q: a dx = 1+ sin(ax) Select one: a. tan(ax) – sec(az) + C b. ax + In | csc(az) – cot(az)| + C c. In |1+…

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Q: Find div F and curl F if F(x, y, z) = 9ei - 3 cos y j + 2 sin² z k. div F= curl F=

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Q: f(seca tan a – 8a")da tan a + a° + c sec a +a8 +e - sec * – a8 +c sec a – a° +e sec a +8

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Q: Evaluate and simplify aluse yuotent rule to Rind US. dxL3x t. / Find. d dx [sec(cos/(1 JCX

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Q: Show that - if W= cos (メ+y)+ Sin(メ-y) Wメメ Wyy ニ

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Q: tan y-1 . sin y- cos y- 1 www. Prove that tan y +1 sin y + cos y+1 2.

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Q: Let F(x, y) = x² + y°, ¤(t,s) = s cos t, cost, y(t, s) = s sin t Then OF 3 -2s? cost sin t+ 3s° (sin…

A: Given: Fx, y=x2+y3xt, s=s cos tyt, s=s sin t To Find: ∂F∂t=?

Q: Value of a(u, v) is, if u = x + y², v = y and x = r cos 0, y =r sin 0 a(r, 0) 2 xr -2x r2 2x2 r -2x…

A: Explanation of the answer is as follows

Q: Find y': y = cot 0 sin 0 O sin² 0 1-tan²0 O1+sin² 0 cos³0 O-1-cos² e sin³0 3

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Q: 5) Find the following of the function f(x,y) =xy+cos y+ysin x

A: To find: The partial derivatives ∂2f∂x2,∂2f∂y2,∂2f∂x∂y. Given: The function is fx,y=x2y+cosy+ysinx.…

Q: Evaluate sin 2x sec*x dx Select one: 8 In| cos x |- 4 sin?x+c - 8 In| cos x |+ 4 sin?x+c 8 In| sec x…

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Q: Choose... cos y = (x sin x - cosx+c) cos y dy = -x sec x dx sec y sin y dy = -x cos x dx (x sinx-cos…

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Q: Compute tan" z · sec² æ dæ. O tan12 z tan10 z +C 12 10 O tan° a tan10 a +C 10 tan12 a sec æ +C 3 12…

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Q: Which of the following is/are linear equation/s of the first order? (2s e) ds = 2 (se - cos 2t) dt…

A: Topic- differential equations

Q: True or False If cos u = cos v, then u = v If false give a counterexample that is true

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Q: v (t) x w (t)=((t)i + (sin t)j + (cos t)k) x ((3t)i + 2k) ijk t sint cos t 3t 02 =(2 sin t)i + (3t…

A: The cross product of two vectors A and B is given by:A=ax i +ay j +az kB=bx i +by j +bz…

Q: fze [sin(3x)]-m(x, y, z), where m(x, y, z) = Part C. yz-1 %3D

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Q: 2) sec?x tan y dy + sec?y tan x dx 0 Ans: cos 2x+ cos 2y = c

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Q: What is the formula for the total distance traveled by an object with a velocity v(t) = sin(t) on…

A: To find the formula for the total distance traveled by an object with a velocity  on the interval .

Q: Of of Let f(x, y) = x°y² tan y Then x +y. equals

A: The derivative of a function of two or more variables with respect to one variable, while the others…