Find the Taylor series expansion for each function for the given value of a.
f(x) = sqrt[x], a = 4
f(x) = e^-x, a = 1
f(x) = x ln x, a = 1
What's the problem? You just directly apply the formula for the taylor series centred around a: $\displaystyle f(x) = f(a) + f'(a)(x-a) + \frac{f''(a)}{2!}(x-a)^{2} + ... + \frac{f^{(n)}(a)}{n!}(x-a)^{n} + ...$
$\displaystyle \Rightarrow f(x) = \sum_{n = 0}^{\infty} \frac{f^{(n)}(a)}{n!}(x-a)^{n}$
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