04: Determine the convergence of tan¹(x) x²+n²In(n+2) , on A = [0, +00).

Q: n cos(n) V1+4n2 (an) at n→∞o or prove that the limit does not exist: (b) In(1+2n²) - 2 ln(1 + n)

A: 7) a) an=ncos(pi n) /sqrt(1+4n2)b) an)-2ln(1+n)

Q: Use the definition of convergence to prove lim {n→∞} (cos n)/(n2-n+1) = 0.

A:

Q: 2) Determine the interval and radius of convergence of 2 '(x+5)** (2n +1)! 34n-1 n=0

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Q: b) Suppose (xn) does not converge to 0. Then there exists e > 0 such that all except for finitely…

A: Let us suppose the following sequence xn=1,0,1,0,1,0,..... We have to see that the odd terms are 1…

Q: Given ſtan xdx = limn→∞ Σ-1 (tan 7)) (7) identify if it is a right k=1 Riemann sum. O True O False

A: The right Riemann sum of integral

Q: Let fn(x) = sin" x and let 8 > 0. a) Prove: fn converges uniformly on [0, 5 – 8], but not uniformly…

A: The given function is fnx=sinnx. To find: (a) fnx=sinnx uniformly or not on given domains.…

Q: For eksample Xn = n² (n+1)! investigate whether the serles Σ 8 n=1 Xn convergent Or divergent. Prove…

A: We will use ratio test to check whether given series is convergent or not.

Q: Q3) a) Evaluate x-23(3x) dr. b) Expand the following function in a Fourier Bessel series using…

A: a) Evaluating the integral  This integral can be solved using integration by parts. Choose the…

Q: Suppose that p(æ) > anx" converges on (-1, 1], find the internal of convergence of p(6x – 9). n=0

A:

Q: ii) Obtain the Fourier series of the function g defined by g(x) = | f(t)dt, justifying your method…

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