11) Test the series for con convergence E (-1)^ sin² (3n) n n=1 = Compute the derivative d br an Since d bn an divergence b= sin² (3n) 2 the sequence The alternating series test us is eventually always 41 is eventually always >1 is eventually always <0 is eventually always 70 keeps changing sign is eventually monotone Is not monotone the series converges the series diverges

Q: 4. The series f(x) = ² - can be shown to converge on the interval [-1, 1). n=1 n (a) Find the series…

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Q: 3. Is it possible for a power series centered at 0 to converge for x = 1, diverge for x = 2, and…

A: We have to tell whether  there exist or not the power series centred at 0 converge for x=1 ,diverge…

Q: (d) By making the substitution x = expu, or otherwise, evaluate S log x dx. 2 cosh² x - 1. (e)…

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Q: Suppose that the coefficients of the power series E an(x – c)" n=0 satisfy |an+1] lim = L. n→∞ an…

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Q: 1 that 1 x" with convergence in (-1, 1), find the power series for with center 1+ 6x7 n=0

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Q: The power series for f(z) = - is 3- z 1 E (z – 2)" n = 0 3- z 1 Σ (3-2)" n =0 3- z 1 2 3"z" 3-z n=0…

A: To Determine :-  The power series for f  z  = 13 - z  is

Q: (x+ 2)" n . Find the interval of convergence of the power series n3" n=0 (A) [–1,5) (B) [–1,5] (C)…

A: Solution:- ∑n=0∞x+2nn 3n un=x+2nn 3nun+1=x+2n+1n+1 3n+1 limn→∞ unun+1=limn→∞ x+2nn3nn1+1n3n+1x+2n+1

Q: orrect answer like that

A: Given,            f(x)=ln(x2+1)

Q: Given the Maclaurin series for cos x : (-1)" -2²n COs x = (2n)! n=0 (i) Find the Maclaurin series…

A: Ratio test to find interval of convergence

Q: Un10)-1 convergent t or diverg 6.

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Q: 1. Given that n=0 power series which converges to (1-x)-2 on (-1, 1). converges to (1-x)-¹ on (-1,…

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