A-Show that S 1, L{cos at} s2+a²

Q: Evaluate L{t cos 4t} s2 +4 b) 52 – 4 s2 + 16 c) s2- 16 s2 - 16 d) s2-4 a) s2 +4 s2 +16 O a O b

A: None of the options are correct

Q: Prove using the IVT cosx = cos-1x has a solution in (0, 1).

A: cos x = x   rearrange to x - cos x = 0

Q: Let u = e-7*sin(7y). Then a harmonic conjugate of u is

A: If two given functions u(x,y) and v(x,y) are harmonic in a domain D and their first-order partial…

Q: Show that the following gn are harmonic and find its conjugate u=3x^2y+2x^2_y^3_2y^2

A:

Q: tan²(z) cos³(z)dæ

A:

Q: 3i +2V2 - 5n -4i +6(1 +a T/4 [(3sec2 t)i - (5 + sin t)j - (6sec t tan t)k)]dt Find 0. 2 2-57T-4 3i +…

A: ∫sex2xdx =tanx+c∫(constant)dx=x+c∫sint dt =-cost +c∫sect tant dt =sect+c tanπ4=1cosπ4=12secπ4=2

Q: 2. [e1/² cos 2tdt Set/2

A:

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: Q4. Let fla) < cos" ( a ) Find fCa) COS n+5 f'(a) = %3D

A: Answer is mentioned below

Q: Show that S COS TX 2x - 1 dx KIN ㅠ 2

A: We transform the integral into another well known integral and then evaluate it.

Q: •2πT 2 cos³ t + 3 cos² t dt

A:

Q: 6. Show that (an)neN C R is bounded if and only if lim supn→∞ an < +∞o.

A: To Prove:  ann is bounded sequence if and only if limsupan&lt;+∞.

Q: Prove | cosz |2 = cos²x+ sinh²y.

A: To Prove: cos z2=cos2x+sinh2y

Q: 1 1 d [x] d [y] Cos

A: To evaluate ∫01∫y1cosyxdxdy Let I=∫01∫y1cosyxdxdy By changing order of integration, it becomes…

Q: Find the first 3 Zerms o Sinx et a =?

A:

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

A:

Q: Prove: L{cos at} = s2+ a?

A: We will prove the given statement.

Q: (a/3 d(cosx) =? 24 - sinx O A) V3/2 O B) 1/2 C) -1/2 O D) -1/3 E) T/3

A:

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

A:

Q: Evaluate the following integrat«

A: Given,               ∫cos4xdx

Q: x is in the interval [0, 2t) * sin2x - cos2x = 0 COS

A: Given: sin2x-cos2x=0; x∈[0,2π) We know that cos2A-sin2A=cos2A…

Q: Show that in the interval (0,1) COS TTX = ∞ TT n=1 n 4n²-11 -sin 2nπx

A:

Q: Evaluate L{3 cos? 2t} 3 3s 3s а) b) 2s + - 2s 2(s2 + 16) 2(s² + 16) 1 c) 3 d) S 3s 2s ' 2(s2 + 16)…

A:

Q: SELBCT ALL APPLICARLE CHC sin A) coverges B) diverges G. HI 20

A: We will use Ratio Test to check congervency

Q: Q6A)If y = cos ¹) prove Zyy + z = 0.

A: See this solution in below

Q: Different substitutions dr a. Show that sin(2r – 1) + C using either Vx - x u = 2x – 1 or u = x dx…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: The functions g(b, c, d) and h(b, c, d) are defined as: g = (b+ c+ d')' + (b' + c' + d') · (b' . c'…

A: