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:
When , it's called a Maclaurin series.
When , 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.
Showing a random 20 of 50 problems.
Example 1
hardEvaluate using Maclaurin series.
Example 2
mediumFind the Maclaurin series for through the term.
Example 3
easyTrue or false: the Taylor series of a polynomial of degree centered at has finitely many terms.
Example 4
challengeUse Maclaurin series to show .
Example 5
mediumUse the Maclaurin series of and to verify Euler's identity in series form: show the real part of equals .
Example 6
easyFind the first two nonzero terms of as a Maclaurin series.
Example 7
mediumWhat is if ?
Example 8
easyWrite the Taylor series of about through the term.
Example 9
easyWrite the Maclaurin series for through the term.
Example 10
challengeApproximate using the first three series terms.
Example 11
mediumFind the Taylor series of through the term.
Example 12
easyWrite the Maclaurin series of through the term.
Example 13
mediumApproximate using the Maclaurin series for through the term.
Example 14
challengeFind the limit using series.
Example 15
hardFind the Maclaurin series of through the term.
Example 16
mediumFind the Maclaurin polynomial of degree for .
Example 17
hardFind the Maclaurin series for and state the interval of convergence.
Example 18
mediumUse the series to estimate .
Example 19
mediumFind the Taylor series of about through the term.
Example 20
easyFind the Maclaurin series of through the term.