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

Q: cos(x) du. u? + 1 When solving• dx using substitution, you got to the integral - cos? (x) 2 Which of…

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Q: sin x – x dx = ? X (a) E(-1)"- 22n (b) E(-1)". 22n+2 (2n).(2n)! (2n +2).(2n +2)! n=l n=1 22n+1 (2n…

A: We have, ∫02sinx-xxdx   It is known that, sinx =x-x33!+x55!-x77!+...

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

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Q: sin x – x dx = ? X 22n (a) E(-1)". 22n+2 (b) E(-1)". (2n).(2n)! (2n +2).(2n+2)! n=1 n=1 22n+1 22n-1…

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Q: A s = e B s = cos(2) C s = e1/2

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Q: S | = cosh (v4 t) s²-2- False True

A: L{ sinat} = as2 + a2,   L{ sin2t} = 4s2 + 42a is falseL{ eat f(t)} = F(s-a) where F is Laplace…

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

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

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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

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Q: Final Answer for a1,a2,and az a, =S° - -1dx +- " 1dx = ? 2n-T 2n (1)()(x) 1 | 1 cos- (1)(1)(x) a1 -1…

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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: COS X -1 dx = ? X 22n (a) E(-1)" (b) E(-1)" 22n+2 (2n +2).(2n+ 2)! (2n).(2n)! n=1 n=1 22n+1 (c)…

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Q: 2 2 sin a dx 1 + cos x O In(2) In(2) O In(4) In(4) -

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Q: Solve the equation 5 cos 0 - 4 = 0 for 0ses 2n

A: Given : 5 cos θ - 4 = 0     for 0 ≤ θ ≤ 2π                                            for 0 ≤ θ ≤…

Q: If f(x) = cos (x) and f(a) = find the exact value of the following. (a) f(-a) (b) f(a) + f(a + 2t) +…

A: Solution)a) f(x) = cos x f(-a) =cos(-a)= cos a f(a) = cos a = 1/6 Hence answer is 1/6 b) f(a) +f(a…

Q: [Pi+1(æ) – Ph-1(x)] dæ

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Q: e sin(x²)dx <e-1. Jo Show that

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Q: The function f(x) = |ax - b| + c|x| : x in (-∞, ol where Find the

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Q: Ex. 17 The value (1+ x) of ] x (1+ xe*)? dx, is equal хе 1 + C (1+ xe*) (a) log + 1+ xe* xe* 1 (b)…

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Q: 6. find the principal value of ln(i + 1) 7. if N = ii, evaluate N

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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: cos x-1 dx = ? 0. (a) (-1)". 22n (2n).(2n)! 22n+2 (b) E-)". n=1 (2n + 2).(2n +2)! n=L 22n+L (c) )"…

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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…

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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

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Q: 2 – sin x |log -п/2 .피2 dx 2 + sin x.

A: Given: I=∫-π2π2log2-sinx2+sinx-exdx For evaluating given integral, we use property mentioned below…

Q: QUESTION 6 Let fo(x) = nx2 +5 for neN and x ER 4n +3 1. Show that (f.(x)) converges uniformly on [ -…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: cos x - 1 dx = ? %3D 22n (a) (-1)". 22n+2 (2n).(2n)! (b) (-1)". n=1 (2n +2).(2n +2)! n=1 (c) (-)".…

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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…