2. (b) Q 3 p sin фа, + p'zag +z cos ф a,

Q: If sin' 0+y cos e sin e cos e and x sin e = y cos 6, prove that x + y* = 1.

A: Solution

Q: 8. If r = sin (ƒ(t)), ƒ(0) = pai/3, and ƒ′(0) = 4, then what is dr/dtat t = 0?

A: Chain Rule d(f(g(x))dx   =   f'(g(x)) . g'(x) We have given r = sin(f(t))        f(0) =  π3  ,…

Q: 28+1 b:If y =-1 prove that. 1- 2y dx

A: # we are entitled to solve one question at a time, please resubmit the other question if you wish to…

Q: To compute sin (3t) cos" (3t) dt, first you need to I Select) * then subsitute u = [ Select ) * and…

A:

Q: 1 y = e*(C, cos2x + C2sin2x) –xe*sin2x a. 2 b. y = e*(C, cos2x + C2sin2x) +xe*sin2x 1 y = e*(C,…

A:

Q: 3. Find dy, where; a) cos(ry) - e 2 elx+y). b) ė?+ Ptany =4, u= xlax (use chain rule)

A: We have to find the derivative

Q: 2. If z y where z= s cos t and y=s sin t, find az/ôs and az/at.

A:

Q: IER, t> 0, u(x,0) sin(87r) cos(90z). u + ru, =x

A: Solve partial differential equation by Lagrange method. Rewriting partial differential equation…

Q: az (b) Determine the by using the Chain rule with the following information: ds z = cos (x"y) – sin…

A:

Q: 7. Differentiate w.r.t x- sin 5x cos 3x

A: Given problem:- Differentiate w.r.t  x sin5xcos3x

Q: snip

A: Given, cosjx,coskx, ∋j≠k, k≥1 if inner product of two function f(x), g(x) on the interval [a,b]…

Q: -3t 10. s = cj e" + c2 e" cos 51 + cz e" sin 51 + 123 O Sm + 5 Su + 17 s - 123 s = 100 O Sm + 17 Su…

A:

Q: If xty= 2e Cos Øand x-y=2ies.m Ø show that Su

A:

Q: B. and , if z = (x² + y²)³/2, and r = e-" sin v, y = e¬u cos v. В. %3D

A:

Q: 2. Let f(r, y,z) = In(r² + 2) + ye* – cos(2yz). Find faya- COS

A: see below the answer as per bartleby guideline we have to solve the first question onl

Q: Suppose f(x, y) : where x = r cos 0 and y = r sin 0. 4 af af and ar Find when r 1, 0 -

A:

Q: Q1: show that1) d/dz [cosz] = -sin z, 2) 1+tan2 z = sec2 z

A:

Q: dt cos (2 sin 21) /1– 4r

A:

Q: 4 cos z Evaluate S 16-y2 ydxdydz

A: To solve the given triple integral ∫0π∫04cosz∫016−y2ydxdydz…

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

A:

Q: 8:54 1 3. If y = (5x)sin(3x) , then %3D dy %3D dx Type here to search

A: This question is related to differentiations. Solve in 2nd step.

Q: If f(x,y,z)=In(x²y+sin² 12

A:

Q: Suppose that w = a7 · exp(2y) · cos(4z) with z- in (+ 5), x = sin (t+ y = In (t +2), z = t.

A:

Q: 4  find The indefinite integral

A: To evaluate the given integral

Q: 4. A force of F(x) = x - cos(3x) + 2,x is in meters, acts on an object. Identify the work required…

A:

Q: b) Is S cos4xv2 – sin4x dx = V(2 – sin4x)³ + C true or false? show me %3D

A:

Q: Q1: show that1) d/dz [cosz] = -sin z , 2) 1+tan2 z = sec2 z *

A: We have to use derivative definition.

Q: Q1: show that1) d/dz [cosz] = -sin z , 2) * 1+tan2 z = sec2 z

A: In both solutions i have used the definition

Q: Compute e4 cos (r – 3) dr with two decimal places. Number

A:

Q: Ex: If w cos(uv), u = = xyz, y = π 4(x²+y²)' aw find at point (1, 1, 1). əx

A:

Q: Suppose f(x, y) = x2 + y? where x = r cos 0 and y = r sin 0. af and Or 1, 0 = 6 Find -when r

A:

Q: 3. Given that z= (u, v), where u 2r cos y and vz sin y. Find and Hence, show that Dy

A:

Q: . Let w- e*² <in Cyz)- e Yz cor Cxz) Find - W X

A:

Q: A particle moves in the xy-plane so that its position at any time t is given by x= cos(5t) and y =…

A: According to the questionx=cos5ty=t3

Q: For the IVP: (1-4) cos ty"-In(r-1)y+VT+5y=e, y(2) =1, y(2) = 1

A:

Q: 3. Show that: • T/2 sin" x dx • T/2 cos" x dx

A: Recall the property of definite integral:

Q: 2 Given that: J2(x)=-, cos.x + sinx find J(x)

A:

Q: show that1) d/dz [cosz] = -sin z

A:

Q: EX/ If f (x)= + COS2X CoS X is Pcx) Continlacaus at x=? %3D

A:

Q: If fex) cos cmx) dx = and %3D fox) E Coscn'x) then %3D COS n3 +! KIN

A:

Q: Find dy/dt. 9) y = cos (rt - 20) A) -7n sinº(nt – 20) C) 7 cos (zt - 20) B) -7n cos(nt – 20) sin(7tt…

A:

Q: 4. Write u = -2 cos Tt – 3 sin at in the form u = Rcos(wot – 8).

A:

Q: -1 If cos x+cos y+cos z= T, prove that x +y +z +2xyz = 1

A:

Q: Suppose f(x, y) = x2 + y? where x = r cos 0 and y = r sin 0. Find and whenr = 1, 6 -: = 1, 0 =

A:

Q: Q1: show that1) d/dz [cosz] = -sin z , 2) 1+tan2 z = sec2 z

A: (1) Use the first principle to derive the derivative of cos(z),…

Q: Let f(r, y, z) = In(x² + 2) + y?e - cos(2y2). Find feyr-.

A:

Q: b) 4 (€) -et cos (dt+물) cos (2dt +물) COS 3

A:

Q: (4) If z = f(r, y) where, a = e" cos v and y = e" sin v, show that (i) dz az e2u. (ii) az 2 2 dz -2u…

A:

Q: 0.5 COS T - In(4 sin z) dz. J0.1

A: