If z2 +2z +23D0 then z=1±i O Z= -1±i O z=2+2i O z=5i-3

Q: (с) 4у" + у %3D 4 sin(3x/2), for 0 <x <л, У (0) %3 0, у(л) — 0

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Q: Find 100 values of S and R obtained from the difference equations: Sk+1 = Rg ( sin (S,)) %3D Rk+1 =…

A: Answer

Q: Find : dw/dk α w=2 sin m ka 2

A: To find dw/dk for the given w

Q: Q2: Evaluate Seas cos²(y s) ds. إضافة ملف

A:

Q: 15. Evaluate 2 (3x + cos 4x) dx

A: The given integral is: I=∫0π2 3x+cos(4x) dx

Q: 2sin 0 d0 2+cos 0 (2+cos 0)²,

A: Given integral is∫02π22+cosθ2+2sinθ2+cosθ22dθ

Q: A particle moves such that its velocity at time t is given by v=3t² i + 2 cos(4t)j + t² k. If its…

A: Given velocity vector: v=3t2 i+2cos4t j+t2 k Position at time t=0 is given by, x0=2 i We know that…

Q: Evaluate: L{cos(3+2t)} s cos3+2sin3 A s² +4 S (B (s+3)² - 4 S (s+3)² +4 s cos32sin3 s² +4 (c) (D)

A: Given:L[cos (3+2t)]=?We know that cos(a+b)=cos a. cos b- sin a. sin b Therefore, Lcos (3+2t)=Lcos 3.…

Q: #/2 |cos" xdx kn/2 If 0 then K = %3D

A:

Q: ー1 B Cos (2 oin (oen 3 + cas の An

A: Sin(A+B)=sinAcosB+sinBcosA

Q: Z2 in H = {0,4,8} find all left cosettes

A:

Q: If z = 2 ( cos 2¥/3 + isin 2¥/3 ), then z^3=   i. 2 - i8√3 ii. -4 + i4√3 iii.-8-i√2 iv. -8 - i4

A: Using de-moivre's formula :

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: -If u = x2 tan-1 २|४ y = - y² tan-1 x 22u дхду x² что - у² + J²u u ә2u u дхду дудх L ala 2

A:

Q: 8. 2/3 cos¹/3 sin dt 0

A: The given integral is;  Cos4/3(t/2) Sin(t/2), limit from 0 to 2pi/3.

Q: Solve for x: 3sin x + /2 cos x: V39 0 < x < 27.

A:

Q: If h (x) = sin (4x) then h 0. V3 V3 2 II

A: Given that hx=sin4x.

Q: Evaluate: L{cos(3+2t)} s cos32sin3 A s²+4

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Q: raluate 1+cos 4r 1-cos 4x

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Q: 3 r = sin 0 + 6 cos 0 О За? + (у — 3)? —— 1 %3D 6æ² – (y – 3)² = 1 D y+6x = ! 1 3. Dy+6x = 3 у+ 3х —…

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Q: O cos Z 12 15

A: Right angle triangle

Q: 32. If 2 sin 0 cos 0 cos 0 =0, where 0 <0 < 2n, then the exact values of 0 are 57 0, 3 O0, 5. 7, ,…

A: Given : 2sinθcosθ - cosθ = 0 Where, 0 ≤ θ ≤ 2π To find : Exact value of θ?

Q: a [Pn (cos 0) | дz rN+1 = −(n+1) Pn+1(cos 0 rn+2

A: To prove that           ∂∂zPn(cosθ)rn+1=-(n+1)Pn+1cosθrn+2

Q: Find 7'(t), given 7(t) - 4e 2t (3 sin(2t), ,4 cos(4t)). F'(t) =

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Q: What is the value of csc ( 1) 137 7T + cos( V3+2/2 O -V3-2/2 -V3+2/2 2 V3-2/2

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Q: Find LT of (i) e(2 cos 5t – 3 sin 5t) 3t (ii) e²ª cos? t (iii) e* sin 2t cos t

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Q: If Z + i sin) then Z²-Z+1=.. = cos 2 b 2- -2

A:

Q: J. (cos x + |cos x| ) dx S. %3D 2

A: see 2nd step

Q: 3 6. Show that [[[ y sinzdxdydz = (1– cos1). 2 COS %3D 00

A: We have to prove given integral

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

A: differentiate with respect to x

Q: Evaluate the integral. 1/2 |[cos 9t i- 3 sin tj + sin? 3t k] dt T/2 | (cos 9t i- 3 sin tj+ sin 3t k]…

A: We have function ∫0π2r(t) =∫0π2[cos9t i -3sint j + sin23t k ]dt

Q: A. Find y' if 1. y = x² cos² 3x

A: y=x2cos23xApply product rule to differentiate the given function y with respect to…

Q: 7. S sin*4xcos64xdx 3 I. 1. 512 3 I. 2046 II. 2048 IV.: 512

A: The given integral is ∫0π8sin44xcos64xdx To solve the integral we first simplify the expression and…

Q: Find ſ z2 sin z dz

A: We can find the integral in the following steps

Q: Find T, N, B, K and t for r(t) = (3csc^3t • sin^6t) i + (3sec^3 t • cos^6t)j + 5k

A: given that                                             r→(t)=3csc3tsin6ti^+3sec3tcos6tj^+5k^ now…

Q: Find all solutions to the equation: [sin(x)+ 1]2cos(x)-3]=0. Зп + 2nk, x = + 2nk, x = 11m + 2nk,…

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Q: r(cos0+isin 0) with 0 (exact) in (0°,360°): а. z = 12-12i Z, =-3-3i z, =-4V3+ 4i b. с. Z3 = %3D

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Q: SR(-1)" – 1)) x – 6n si 6T < x< 7n cos nx = { 8п — х si 7п <x< 8п n=1 +

A: The Fourier series of the function fx on -L,L is as follows. fx=a0+∑n=1∞ancosnπxL+bnsinnπxL. Use the…

Q: Q/ IF y = Sim ܠܐ 10²² (4) y = 3/² sin(x) cos(x) Prove that

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Q: F.(3e-7 cos(3x')) is equal to 3. T9+o 1 -7 cos 12 4 O b. 2 3, T9+o 3 cos 9, 12 4. 12 3. 2 COs Va 4+o…

A: Using the Fourier cosine transform table, the following formulas can be written.…

Q: + 8z7 – 5 sin z)dz O 4e -z +5cos z +e O 4e +z" +5sin z +e O 4e +z* - 5sin z +e O 4e +z – 5 cos z +e…

A:

Q: 37. y = (2x + 1)V2x + 1 38. y = 20(3x – 4)'/4(3x – 4)-1/5 3 39. у %3 40. y = (3 + cos³ 3x)-1/3 %3D…

A: Explanation of the solution is given below...

Q: Evaluate L{cos (3+2t) } scos3 + 2sin3 A s2+4 scos3 – 2sin3 B s2+4 (s+3)2+4 (s+3) 2–4

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Q: 7T If 0 = then %3D 4 sin(0) = %3D cos (0) %3D =

A: Given that              θ  = 7π/4 Here we have to find         sin(θ) and cos(θ)

Q: 4e + 6x° + 9 cos z)dr %3D

A: Given

Q: Consider the model Yi = β0 + β1Xi + εi, where E(εi) = 0 and Cov(Xi, εi) = 0. We observe (Yi, Xi)…

A: Given Model is y=β0+β1Xi+εi where, β0= Intercept Parameter β1=Slope parameter εi= random error…

Q: Solve the diffesential equation 2ber 十X

A: