Lee fiR-> R continonsliy diffenentiable functionwi4th penod aT * fx+21) = f(x) and factan) %3D also Fdx = 0 Use the fourler sepiles and Parsevall's identities prove killowing to inquality 23 write out f)ni and fCx) in their full series to determine A. md C. A and Die then use each o efficlent to determine relwtion between and bic und Ca io7 fa) = Ao +$ Ak cos Ckx) t Bx sin (ka) 2 f'(x) = t. to E Ck CosCkx) t DK sin(ke)

Q: Prove LHS=RHS

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Q: determine the nature of functon for even and odd Ax) = log(x+ Vx² +1) ?+1)

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Q: Prove. Show all steps to get to ln (2^(-2n))

A: Step 1: Given data :The expression is represented as, ln(BA​)=ln(((2N)![(N−n)!]2)(N!)2(2N−n)!​).…

Q: 2) Prove that: d? L„0) = n;(n – 1) %3D dx²

A: Consider the given information: Let Laguerre polynomial is given by, Lnx=∑k=0n(-1)kk!nkxk…

Q: Fourier Series of 2 on the interval [-T, 7 3

A: Fourier series of function fx on interval -L≤ x≤ L is defined as: fx=A0+∑n=1∞ An·cosnπxL+∑n=1∞…

Q: (log n)* lim

A: Explanation and solutions is given below....

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Q: Q4) Considering fanction of fla)=x, & -ncacrR a) Is this function odd or even b)epand fantion sine…

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