1. Use the residue theorem establish the identity: 1 et + e- -da = t|2 플

Q: What is the domain of sech-1 x? How is sech-1 x defined in terms of the inverse hyperbolic cosine?

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Q: Evaluate f sin(5/z) -dr Select one: a. 금cos(5/z) + C b. 5 cos(5/a) + C – cos(5/x) + C C. d. cos(5/2)…

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Q: Pow thal lel; and onlr

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Q: use Theorem to find 31) F(A) = 4t? 5 Sin 34

A: To find the Laplace transform of the below function using the theorem. ft=4t2−5sin3t

Q: Ex:. Find the fourth roots of Z=-di Say no 4 K = 0₁12₂3

A: given z=-8i To find the fourth root of the given complex number proceed as follows comparing the…

Q: Which one of the following is equal to Scot (™) do? 2 ○ 2/4 sec² \sin (12) ○ 2) | + c 2 In sin (18)…

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Q: C. lim x→1+ 5x 4 31 -1-x 3x]

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Q: Q3 Find and show the work for (x+3)(3x+2) dx. (a) х (b) F (sin(2x) – cos x) dx. (c) S(3x² + 2x +…

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Q: ] Prove that the equation 2" – x = 1+ 4/x has a solution greater than 0.

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Q: (ez²-1-7²) Sin³z

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Q: tan² 0 – sec² e :

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Q: prove thati- Exi 2. (Exi) 2. (xi-X

A: Solution-: We prove that,

Q: Prove that a b π √√(x − a) (b − x)dx : = (b-a)² 8

A: To prove that,  ∫abx-ab-x dx=π8b-a2

Q: Let F = (2yz – 3x) i + (3xz + 3y) j – (2xy+ ∞z) k. Find div F and curl F.. |

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Q: Fra) = Sin (2t) Find the 7h taylor Polynomial of

A: Given function is  Fx=∫1xsin2tdt

Q: (c) (z-a)", where a EC and n = N*

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Q: Q. : Find the radius of- Co nvergence and the interval of Co nvergen ce (x - 2 )" In cn+4) & W

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Q: Q3) a) find f sec³ x dx

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Q: Use substitution to evaluate the integral 4 sec2 4xvtan 4xdx 4 (tan 4x) + C 3 15 (tan 4x) + C 2 (tan…

A: Given query is find the value of the integral.

Q: -sin xdx

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Q: tan75∘=(√A+1)/(√B−1) A= B=

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