Series for sin 1r Integrate the binomial series for (1 to show that for x < 1, x²)-1/2 0 1:3.5. ... •(2n – 1) x2n+1 · •(2n) 2n + 1' sin-x = x + ... 2.4.6. n=1

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A: The Maclaurin series of tan-1x is tan-1x=x-x33+x55-⋯

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Q: 1 (a) Use the Integral Test to show that > converges. 2. n' +1 d 1 n = 0 -1 tan dx Hint: 1+x?

A: As per our guidelines, we are supposed to solve only one question.  Kindly post other questions  as…

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A: Let's replace x by x2 to obtain: Let's now expand up to four terms to get:

Q: 3. Find the derivative of the series (-1)**'2" -x2n+3 n=0 n!

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Q: 24. Let f be a function such that f'(x) Maclaurin series for f? = sin 9 (A) x - + 10 216 9 X (B) 2x…

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