1. Determine whether the following series converge or diverge with proof.
a. e. k2)]
2. Determine of the following series converges conditionally or absolutely.
3. Determine of the following series converges conditionally or absolutely.
4. Find McLaurin series for the function f defined by f(x)
5. Find a power series representation of the function f defined by
centered at a = 2.
6. Find the Taylor series for f(x)=In(2+ x) with center a =-1. Find the
interval of convergence.
7. Find a power series representation and determine the interval of
convergence y = sech x at a In(2).
8. Use a power series representation to calculate the following limits and
tan x - x
( arctan(x²) xx
9. Approximate fby a Taylor polynomial with degree n at the number a. Use
Taylor's Inequality to estimate the accuracy of the approximation of f when
x lies in the given interval.
f(x) = In(1 + 2x), a = 1, n = 3, 0.5b. a 0, n = 3, 05x501
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