1. Find the Maclaurin series for the function x2 In(4+ x). Also find the associated radius of conver- gence. following funcetions centered aISSOciat adius

Q: Σ(51) k

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Q: 9) Σ=1 10) 3/3 - (-1)^(1+n²) n! 3 1 4 2 11) Σ.» (= − 1) =0 τη 13) Σ=1 14) En=1 15) En=1 Σ + n+1 12)…

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Q: 1 Σ n%3D1 n

A: The given series is ∑n=1∞1n-1n2n To find: Find convergence or divergence of the series.

Q: Give an example of a series that diverges by the Ratio Test

A: Given query is to give and example of series that diverges by ratio test.

Q: Use your knowledge of geometric power series to find a power series to represent the function 3 3x +…

A: Given   Centered around 2. Find the sum formula For the geometric series

Q: 2" (r+1)" n=0

A: We have to find the values for x which the series converges and Sum of the series for those values…

Q: s of x for which the series converges. 87 n=1 < x <

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Q: 8 s=2 s(s + 1) s2 + 1 75-1 = 00 Σ m=# C(m) xm

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Q: Evaluate the series or state that it diverges.

A: Given that : The series ∑k =0∞  116k2 + 8k - 3 . First factoring the denominator term,…

Q: sin x dx

A: Consider the given integral.

Q: Let Ea, be an infinite series whose sum is s. Which of the following ast be true of s? 100 lim Vla.…

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Q: Identify the interval on which the series is valid.

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Q: centered at 3. Find a power series representation of 1+x

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Q: Expand the function

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Q: n E(-1) n n=1

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Q: x soo x = (x)ų

A: The function is: hx=xcosx We have to find the Maclaurin series for the given function.