Practice Taylor Series in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A representation of a function as an infinite sum of terms calculated from the function's derivatives at a single point: f(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(a)}{n!}(x-a)^n
When a = 0, it's called a Maclaurin series.
When a = 0, it's called a Maclaurin series.
Approximate any smooth function with a polynomial by matching the function's value, slope, curvature, and all higher derivatives at a single point. The more terms you include, the wider the region where the polynomial closely matches the function. It's like fitting a polynomial glove onto the function's hand.
Example 1
easyFind the Maclaurin series for e^x up to the x^4 term.
Example 2
hardFind the Maclaurin series for \ln(1+x) and state the interval of convergence.
Example 3
easyWrite the first four non-zero Maclaurin terms for \sin x.
Example 4
mediumUse three terms of the Maclaurin series for \cos x to approximate \cos(0.1).