Taylor and Maclaurin Series Lecture Video
1. Find the Taylor series for \(f\) centered at \(3\) if \(\displaystyle{f^{(n)}(3)=\frac{(-1)^{n} n !}{2^{n}(n+1)}}\) solution
2. Perform operations on a known Maclaurin series (i.e., use the provided table) to
find the power series representation for each function \(f\). Include
the interval of convergence.
(a) \(\displaystyle f(x)= x^2 e^{-2x}\)
solution
(b) \(\displaystyle f(x)= 3\sin(2x)\)
solution
(c) \(\displaystyle f(x)= 4\cos(x^2)\)
solution
(d) (i) \(\displaystyle f(x)= xe^{-3x}\) (ii) \(\displaystyle f(x)= 4x \sin(2x)\) (iii) \(\displaystyle f(x)= 2x \cos(x^2) \) solution