n=1 n=1 A n=2 nen (−1)” cos(n) n2 1 n(ln(n))

Q: L {e-2 sin(2t) + e³¹12} L {(1+e-¹)2} L {tet cos(5t)}

A: We will find the required  Laplace transformation.

Q: In3 X (a) I e dx In2 dx x(log x)² (b) S 元_2j元_4 cote (C) S (1 + e 2 )csc Ode

A:

Q: A s = e B s = cos(2) C s = e1/2

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Q: Express z = -2+4i in its trigonometric form

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Q: f6sin(x) cos(x)'dx.

A:

Q: Prove the identity. sinh(x + y) = sinh(x) cosh(y) + cosh(x) sinh(y) sinh(x) cosh(y) + cosh(x)…

A: Given identity for proof is  Sinh(x+y) = Sinh(x)Cosh(y)+ Cosh(x)Sinh(y)

Q: Using (11) and (12): 1 dx 1+ cos x tan +c

A:

Q: L. Let h (x) = f (x) g (x). Find a. h' (1), b. h' (3), and с. h' (4).

A: According to the given information,

Q: 4 4 x tan?(x) dx = %3D Jo

A: Given definite integral is ∫0π4 4xtan2xdx. By Integration by parts, consider u=x,v'=tan2x.

Q: (a) Suppose f(x) = cos (15x) b* and f'(0) = 2. Find b. 2 The value of b is e (b) Suppose f(x) = sin…

A:

Q: y (5) +y (4)-y'-y=0, y (0)=0, y'(0)=0, y" (0)=1, y 3) (0) =0, y (4) (0)=0

A:

Q: y = cos(x In 3) log3 (sin x) is: y 3D cot(x) cos(x In 3) – sin(x In 3) In(sin x) y' cos (x In 3) -…

A: As we know that; The Chain rule: fgx'=f'gx·g'x The Product rule: f·g'=f'·g+f·g'   And ddxlogax=1xlna…