22 prove that the taylor series converges to f x by

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22. Prove that the Taylor series converges to f ( x ) by showing that ( ) 0 as n R x n   .
24. Prove that the Taylor series converges to f ( x ) by showing that ( ) 0 as n R x n   .
30. Use a known Taylor series to find the Taylor series about c = 0 for the given function, and find its radius of convergence.
4. Use an appropriate Taylor series to approximate the given value, accurate to within 11 10 .
8. Use a known Taylor series to conjecture the value of the limit.
12. Use a known Taylor series to conjecture the value of the limit.
2 0 1 lim x x e x 2 2 0 0 1 (1 2 2 ...) 1 lim lim 2 x x x e x x x x   16. Use a known Taylor polynomial with n nonzero terms to estimate the value of the integral.
18. Use a known Taylor polynomial with n nonzero terms to estimate the value of the integral.
24. Use the Binomial Theorem to find the first five terms of the Maclaurin series.

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