5. Use residues to evaluate the follo 1 2 a) * : OP 3 sin 0 + 5

Q: Evaluate L{3et sin 2t} 6. a) s2 + 4s + 8 6. b) 52- 4s + 8 c) s2 + 4s – 8 s-4s - 8 a 6o

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Q: .) what is the remainder when 1't2°+ 33 t... + 1000° is divided by 6.

A: We need to find the remainder when 13 + 23 + 33 + ........ + 10003  is divided by 6. We know that ,…

Q: Show that f Va²-t²dt = a² sin-¹(2) + x√a²-x².

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Q: Show that sin a – sin b < Ja – b), for all a and b. (Hint: MVT) use -

A: Mean Value Theorem :  The mean value theorem states that a function f which is continuous on the…

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: a) 2 cos x - √√3 = 0

A: a) The general solution of  cosx=cosα  is  x=2nπ±α    where , nϵZ  in given question, 2cosx-√3= 0…

Q: 2. Suppose ALXry) = 2xy-ix"y. Find D.A

A: We have to find out ∇.A

Q: er j70 a) sin(70) = 7(e+e °) b) cos(70) 2 con ej +e j0 c) cos(0 + ø) = te jø 2 (ej0 te j°) (ej®+e…

A: Use exponential form of sine and cosine

Q: - 75ec 3x+tan 3x(sec 3x+tan 3x) cos 3x dx (7sec 3x+tan 3x)In 7 + C 7secax+tan ax + C 7 In 3 3 O c B…

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Q: which expression below can be obtained from 8sin squared(3x) by using a power reducing formula?…

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Q: Determine the area that lies under f (x,y) = 9x² + 4xy + 4 and above the rectangle given by [-1,1] ×…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: sin 0 If 1+cos 0 x2 x2, then tan 2 - a) b) 4 c) x2 + 1 d) x2 |3| 2.

A: Given,  sin θ1+cos θ=x2 To determine tanθ2

Q: What is cos A B C D 5T 6 1 ? 1 2 2 √3 2

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Q: See the attached file (12 12)Find the integral f (1 – sin? 4x) cos 4x dx A)sin 4x – sin? x +c B) -…

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Q: lim, o (cos z)= takes which indeterminate form? А. 100 В. 00 С. оо D. Е. 1 х о 8 -18

A: Here, we can solve it by taking the limit of individual terms.

Q: | a 0.24) tan(sin-1x) = b) c) =x d) 1 - x2 3

A:

Q: T/2 S [costi-sit cos ti – sin 2tj +sin? tk |dt.

A:

Q: 4. Find the domain aud of the following tenctions; a)1 cos(x-) -メ+ パーイ イー+an×

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Q: forieiz)=r(2 - CoS 20) rz + %31 2 of of de find of 150 7.

A: Suppose f  is a function of x,y and z variables . To find partial derivative of function with…

Q: 7 |sin? xdx 2 |sin? xdx 11 Ssin? xdx

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Q: S sin2xsin6xdx

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Q: What is sin (20) d0? а) 1 b) 0 1 d) 3 8 c) f) None of the above 8 2.

A:

Q: de a+bcose' where a> bl. Hence or otherwise evaluate 2n de √√2-cose 3

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Q: 7) 3sin²x - cos²x = 0

A:

Q: The f sec$30 sin 30 d0 is {A} sec*30 + C 12 {C}-cos*30 + C {D}cos 30 + C 12 {B} sec 30 + C 18 18

A:

Q: п If z = √3 (cos 5T + i sin 57 ) then 2² 6 5π a) 3 (cos + i sin 577) 12 12 b) 3 (cos 5+ i sin 5) c)…

A: Given that z=3cos5π6+isin5π6

Q: (Dª + 5D² + 4) y = 0 a. y = c1e“ + c2 cos x + c3 sin x + c4e¯ b. y = c1 cos x + c2 sin x + c3 cos 2x…

A: To find: The general solution of differential equation D4+5D2+4y=0. Given: The differential equation…

Q: Sin (x) n=

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: The answer of integ ra Ssinzx cos3% dX

A: We have to evaluate the given integral.

Q: Evaluate [cos² ydy a. 1/2y + 1/4sin2y + c c. 1/2y + 1/2sin2y + c b. 1/4y + 1/2sin2y + c d. 1/9y +…

A:

Q: Ys l.2 Sin(o+꽃)

A: r=1-2sin2(θ+π3)