6) S sech? (2x- 3) dx | ex-e-x 7) S ex+e-x 8) S(eax – e-ax) dx sinh x 9) S dx 1+cosh x 10) ſ csch? x coth x dx

Q: Find the derivative of the following functions and simply it whenever possible. 1. y = 34x

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Q: /3 In (x+ 1) e series representing the integral -dr is given by A. (-1)"+1 n=1 3" (n+ 1)2 В. (-1)"+1…

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Q: Find the derivative of the following functions and simply it whenever possible. 2. y = log√(2x+5)

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A: Here is the solution:

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Q: whole number.)

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Q: 1. Find the Laplace transform of eat and 1 for t is greater than or equal to zero.

A: follow the procedure given below.

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A: Please find all your answers in the conclusion.

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Q: 2 dt 22. Evaluate o v9– 2t² 2 dy 3-y³ 24. Evaluate o v8-y'

A: 22)I=∫0129-2t2dtt=32 udt=32 duI=∫29-9u2 32duI=2 ∫11-u2 duI=2 sin-1uI=2 sin-12 t301I=2 sin-1(23)

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A: Here is the solution:

Q: tan zdr

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Q: x"+1 has the radius of 5, then the radius of convergence of the If the series >. "n+1 n=1 series a…

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Q: Find the inverse Laplace transforms of the functions: a) F(s) = 9+s/4-s^2 b) F(s) = 1/s(s^2+4)

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Q: Find the derivative of the following functions and simply it whenever possible. 6. y = ln(ln sec x)

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A: This question can be solved using the concept of derivative of hyperbolic function.

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Q: Use the equation giving the flux of the vector field across the curve to calculate the flux of F(x,…

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Q: Linear equation of order one: dy-(x' -2xy kdx =0 Integrating factors fouund by inspection.

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Consider the vectors: å = ỉ– 3j + 2k , b' = 4j – 2k and ở = i + k in 3D A. Write 3a – 4 b - 2¢ in a…

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