QUESTION 8 Use residues to show that P.V. S zsin z ²+2x+2° -dz= (sin 1- 1+cos 1).

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

A: Answer

Q: i. An V21+3n an = 2¬" coS NT

A: We have to check whether given sequence is convergent or divergent. If convergent then find it's…

Q: Find the Grodient (Cylindrical ) V=(2pz?sin"p)op +(pz-sin24)ap + (2p2 sin? o) az

A: Given: V=2ρz2sinϕaρ+ρz2sin2ϕaϕ+2ρ2zsin2ϕaz To find: Gradient of given function.

Q: In Laplace transform Llt?e2"sin3t]= O a. d² L[sin3t], 5+2 ds2 O b. ds L[sin3t],s-2 O c. d2…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: @CDX-4Dx Dy + 403ju= sin(ex+y) Ans. u=dily+2x)+x$zly+2x ) + sinfexa:

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Q: ind positive constants b and n, such that 3n + 2 n.

A: Finding the values of b and no

Q: ot/x csc Jx = xp csc x+C 2/x O csc x+C O -cof x+C O 1 cot/x +C

A: We will use substitution to solve this

Q: 2" cos(r) dr.

A:

Q: 1. Calculate ln(-/2) and acos(2).

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Q: -2n 1 9. Evaluate : de 6+ sine

A: Given, ∫02π16+sinθdθ=2∫0π16+sinθdθ Let us take…

Q: 10. Prove that 7/2 sin 8 cos (cos a cosec 0) de =- (1-cos a). CO TE/2-a

A: We will use the Differentiation under Integral sign method, to solve the problem.

Q: Ca 3+1) cos ca 4+4x)dx

A: To solve ∫x3+1cosx4+4xdx

Q: Equation: Answer:

A: We want to find value of x. For this we use Pythagoras theorem, which states that Hypotenuse2 =…

Q: Find [2 Cos 30° + i sin 30⁰ Y = 2 n=s 0 = 30 5

A: De Moivre's Theoremif r(cosθ+isinθ) is a complex number, thenrcosθ+isinθn=rncosnθ+isinnθ

Q: 10. Prove that 7/2 sin 0 cos ! (cos a cosec 0) d0 /2- TC (1-cos a). COS

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Q: sec-+2sin 4 7 π. (cot)cos( 3 5. [K4] Determine the exact value for 2T.

A:

Q: Prove that v2 cos(20+45°) = cos e-2sin Ocos 0-sin 0, where 0 is measured in degrees.

A: *formula:- cos(A+B) = cosA*cosB - sinA*sinB. sin2A = 2sinA*cosA. cos2A = cos^2(A) - sin^2(A).

Q: Evaluate (s 2'ds Oa 2 1) In2 Ob. 2 (sln2 - 1) (In2)2 O. 2(sin2 - 1) (In2)2 Od 2° +1) In2

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Q: de 6) S 7) S(1 – sin? 3t) cos 3t dt 8) ſ tan (5x) sec?(5x) dx cos? e

A:

Q: 2 2 (5 cos? r* sin 0 drdodo: Tame 0 01

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Q: dt 1. cos (2 sin 2r) V1-4r

A:

Q: I sin r cos xdx. 6. Evaluate sin ¹3 3

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Q: tan(a+β) ; cosα = −(11/61) for α in Quadrant III and sinβ = −(63/65) for β in Quadrant IV

A: To find: tan(α+β)

Q: The population of a community is known to increase at a rate proportional to the number of people…

A:

Q: S+ V D 1) cos (x +V x )dx = OA. 5 2. sin(x + Vx) + C Ов. 5 sin(x + 2 VxF) + C Ос. 2 sin(x + Vx) + C…

A: We have to determine the integral of the given function.

Q: 1-sinx If y= find y'. 1+sinx

A: We can use the quotient rule to find the derivative of this function.

Q: S™ sin dt Sa" 2 1 b. 2 С. 3 d. None of the above a.

A: Given that, I=∫02πsint2dt we have to find the value of given integration.