х. у 2) w=¨+2,x= cos“(t), y = sin°(1), z =-, at t = 3 Z Z t

Q: 4 TT 37. tanα < a < T; cos B = 2' 50 < B < -- %3D 3 2 2

A:

Q: 19.Show that W[eλt cos(μt), eλt sin(μt)] = μe2λt.

A:

Q: (s,+)=(-3,1) X=5?+2+? y= 6st a) 4s x sinly) + 6+x?coscy) at (-3,1) b.) 8tx Sincy) + 6sx? Coscy> at…

A: GIVEN  (s,t)=(-3,1) X=s2+2t2  Y=6st substituting the value of s,t for X and Y we have  X=(-3)2…

Q: z = 2e"žsinx – 3e*cos(y) Ве find: www a²z a2z (n az а) дхду"") дудх ,b) ду

A:

Q: Two waves travelling in the same directio are given by: y1 = 0.2 sin(2ttx-20t+0) and

A: Given,  two waves travilling in the direction are                     y1=0.2sin(2πx-20t+φ)…

Q: If u(t) = (sin(2t), cos(2t), t) and v(t) = (t, cos(2t), sin(2t)), use Formula 5 of this theorem to…

A:

Q: If y(u) J5 COs v9 dv then cos(9u eIu y'(u) = %3D e4

A:

Q: Suppose that S"(ax + b) cos x dx then the value of a equals

A: Given,           ∫0πax+bcosxdx=6To find: The value of a.

Q: If u(t) = (sin(4t), cos(2t), t) and v(t) = (t, cos(2t), sin(4t)), use Formula 4 of this theorem to…

A: Find u(t) . v(t) first then differentiate with respect to “t”.

Q: If z = +i then Im(coshz) A) –sin1sinh4 B) cos1cosh4 e* +e* C) cos1 2 D) sin1cosh4 E) sin1

A: Topic:- hyperbolic function and complex number

Q: Find the value of zrr at the point (0, 3, 2) where x²y? + z² – cos(xyz) = 10. |

A:

Q: 9. y = C,eax cos(bx) + C2eax sin(bx); a and b are parameters

A: As per our guideline we are supposed to answer only first asked  question. Kindly repost other…

Q: // Show that y" + y = 0, given that y = 2 sin x + 3 cosx

A: First find the first and second derivative of the given function then simply put and simplyfy

Q: b) Describe, the motion of a particle with position (x,y) as t varies in' tthe given interval X= 5+…

A:

Q: L[cosh(@ot) u(t)], C[sinh(@et) u(t)] and L[cos (@t) u(t)

A:

Q: Show that y" + y = 0, given that y = 2 sin x + 3 cosx

A:

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

A:

Q: S sin³x /cosxdæ =? O a. ( ?cos'z – cosz) vcosa + C O b. ) +c rt), O d. (cosr + cosz ) /cosz + C C.

A:

Q: 0° S (c) Prove that: 2cos 20. cose 2 + 2 tan0. sin0 = %3D cos?e – sin? e cose o AEGW is drawn.

A:

Q: If A=2(1-cos 0)â, – pyâ, (1– cos ¢)â, – ppâ, +zcos² þ⸠, what is 4 8. V•A ?

A:

Q: 3) if y= CoSX then shift it by a) left TC b) Down1, lett 2

A:

Q: ad boda noY BAJUM 7. Find dy/de. dimil nom y = sin [cos(tan 0)]

A:

Q: If  sin⁡x=e^y,  0<x<π, what is dydx in terms of  x?

A: Given sin x = ey   ..................(1) Differentiating both sides with respect to x  d(sinx) / dx…

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

A: Given ut+xux=x2 By Lagrange's method , we get dt1=dxx=dux2 By equation (1) and equation (2) , we get…

Q: 1. If Z = sin r+ 2 I+1 6. - ", find dZ/dr.

A: differentiate with respect to x

Q: If z = x2 + y? x = e' cos(s) and et sin(s y = ), then

A: ∂z∂s=∂z∂x∂x∂s+∂z∂y∂y∂s Lets find out each derivative z=x2+y2∂z∂x =2xx=etcos(s) ∂x∂s=et…

Q: (3 cos t – 1)i + (2 sin t + 3)j,

A: We sketch the curve as

Q: Given f(x,y,z) = cos(4xy) + sin(4z). Find fx(8,9,0). Leave your answer correct to two decimal…

A: Solution

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: ) // Show that y + y = 0, given that y = 2 sin x + 3 cos.x

A:

Q: 7a6(cos +i Si ) IF USE DE MOIURES TheoREM To Find Z. 23

A:

Q: (2 cos t, 2 sin t, t), where 0 <t < .

A:

Q: 8 cos (2r² + 2y²) dy dr Hint You could take a cab to the pole.

A: Given the integral is ∫02∫04-x28cos2x2+2y2dydx

Q: 19. For all positive angles less than 360°, if csc(2x +30°) = cos(3y- 15°), the %3D sum of x and y…

A: Given that csc(2x+30°)=cos(3y-15°) It is known that csc(x)=1sinx. So, 1=sin(2x+30°)cos(3y-15°)…

Q: Given f(x,y,z) = cos(5xy) + sin(4z). Find fx(6,6,0). Leave your answer correct to two decimal…

A: Given f(x,y,z) = cos(5xy) + sin(42). Find fx(6,6,0)

Q: Find the distance traveled by a particle with position (x, y) as t varies in the given time…

A:

Q: -41 sin tZ dz, c: 1Z-il=2 z4 ans: 3. coshz dz ,C: IZ1=1 27T ans :

A:

Q: Which is equivalent to ſ sin y cos(/2) dy? C/2) dy? a.) S [sin("/2) – sin ("/2)] • dy b.) S sin("/2)…

A: The given integral is: I=∫sinycosy2dy As according to trigonometric formula:…

Q: 22. Find the value of arcsine ( 2x + y ) given that TT sin-( 4x + 3y ) = 2 cos ( x + y ) = . TT and…

A:

Q: 9. Jer'y ds, C:x cos t, y sin 1, z = 1, 0<1s/2 %3D 77

A:

Q: 3) Show that y" +y = 0, given that y = 2 sin x + 3 cosx

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: .2π π 1 -εrocos? θ r dr sinθdθ φdφ x 32 πο X = ?

A:

Q: Determine cı and c2 so that y(x) = c1 sin 2x + c2 cos 2x + 1 will satisfy the conditions y () = 0…

A:

Q: Given, w=2iz - sin iz. Find i dz 2+ cos iz -2- cos iz -2+cos iz -2+cos z

A: image is attached

Q: Sketch X,(t) and Xa(t) Where X,() = - Sim3t Sin3t %3D 3. X,(e) = /a Sin 3t %3D

A: To draw the graph of functions X1(t)=-13sin3t and X2(t)=13sin3t, substitute different values of t in…

Q: 22-j is 1. -1+jZ If Z = cos 0 + j(1+ sin 0), show that the magnitude of

A:

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

A: Solving given partial differential equation by Lagrange method. Rewriting partial differential…