A/ Show that as a half range series of cosine terms for 0 < x < 1, π² /cos 2x cos 4x cos 6x +- + -...) 6 1² 2² 3² x(π-x) = = +

Q: EX: - Derermine expoentail fourier series of X(t)=exp(2t) for -1<t<1 and has period of 2

A: Find the attachment for the solution.

Q: Apply Maclaurln's Serles to Show (-1)*-1,2=-2) 2(n – 1)1 cos X=

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Q: (3Vr + 2e) dx.

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Q: + tan dy 37 Ify = tan -1 -1 1 2 x +5x+7 1 2 1 2 1 2 x² + x + 1 +... to n term.

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Q: 25. The height of a wave can be represented by the function y = 3 cos ((2 - 6)) + 4, with time in z…

A: The equation represents a periodic function. The height is represented by and time in hours is…

Q: Q1) Show that: (b) (cosx) = -sinx =1+* (a) (1+x) =1+6x %3! (e) (VF) = (d) v1+ tan x

A: Note:  We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: If csc e = 1/3t, then where defined, cos 0 A) Square root of (1 – 9t²) 3t/squareroot of (1 – 9t2)…

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Q: lim as x approches 0 of cos(6theta)-1/sin(7theta)

A: Given: fθ=limθ→0cos6θ-1sin7θ Apply limit by substituting θ=0 in the above expression.…

Q: e2 6. - dx -Find 1

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Q: 1 1 Prove 2 csc? x 1- cosx 1+cos.x

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Q: find the series of cosx4 and (cosx)4

A: The series for cosx is cosx=1-x22!+x44!-x66!+...

Q: 5.) Scosx (69425 Jax Са (9 + 25 sin(x) dx

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Q: If Z= (cos0 + isinO) (cose+isine)^n Find 1+ (cos0 + isin0)^2n

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Q: Find sin a. (-/5 ,2) [ ?] 1

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Q: Q/ Evaluate the following functions 1.In(3-16) 3. cos ¹ (1+i 3) 2 (3|0.52) 2. e ‚4. tanh¯¹ (2-i5)

A: According to the given data, evaluate the functions:

Q: Expand ?(x) = x2, −1 < x < 1 into an appropriate cosine or sine series

A: Given,fx=x2   , -1&lt;x&lt;1

Q: The value of (-1+√3 i)^(1/3) is О 2 exp((2TU/7)^i ) 2 exp((2/3)^i) 2 exp((2T/9)^i) 2 exp((2T/5)^i)…

A: We need to choose correct option. As per Bartleby's guidelines we can solve only one question from…

Q: 1 dx ½ x* -1 1 a) arctan -In 3+ 3 4 8 1 b) -arctan 3 --In 2+ 3 4 8 c) -arctan 3 +-In2+ 4 8 1 1…

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Q: P(A)=0.3, P(B)=0.6, A and B are indep, find P(AB'), P(A|B')

A: We have given that  P(A) = 0.3 P(B) = 0.6 If A and B are independent then, P(AB) = P(A and B) =…

Q: 13.) Find a power series for the function f(x): = 5 2-6x3*

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Q: - In-2. Hence show that In = 01 tan" x dx = n - 1

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Q: nd Maclaurin for Series frax)= sin X

A: Given we have given the function  f(x) = sin(x) we have to find the Maclaurin series for f(x) we…