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### Section 4-16 : Taylor Series

For problems 1 & 2 use one of the Taylor Series derived in the notes to determine the Taylor Series for the given function.

1. $$f\left( x \right) = \cos \left( {4x} \right)$$ about $$x = 0$$ Solution
2. $$f\left( x \right) = {x^6}{{\bf{e}}^{2{x^{\,3}}}}$$ about $$x = 0$$ Solution

For problem 3 – 6 find the Taylor Series for each of the following functions.

1. $$f\left( x \right) = {{\bf{e}}^{ - 6x}}$$ about $$x = - 4$$ Solution
2. $$f\left( x \right) = \ln \left( {3 + 4x} \right)$$ about $$x = 0$$ Solution
3. $$\displaystyle f\left( x \right) = \frac{7}{{{x^4}}}$$ about $$x = - 3$$ Solution
4. $$f\left( x \right) = 7{x^2} - 6x + 1$$ about $$x = 2$$ Solution