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Overview
Advanced Mathematics and Calculus 12 (MAT611B)
Calculus
12. Use linearization and Newton's Method to solve problems
12.7 Taylor polynomials
Taylor Polynomials: Formula and Approximation
Learn how the taylor polynomial formula builds polynomial approximations to functions, including the special Maclaurin polynomial case.
What You'll Learn
Identify the Taylor polynomial formula and what each derivative term contributes.
Recognize a Maclaurin polynomial as the special case of a Taylor polynomial centered at zero.
Calculate a second degree Taylor polynomial by finding a function's value, first derivative, and second derivative at the center.
Apply factorial coefficients correctly when building higher degree terms of the polynomial.
Compare a Taylor polynomial's graph to the original function to see how the approximation improves near the center.
Solve for Taylor polynomials centered at nonzero values, not just at zero.
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Learning resources
PEI Curriculum Aligned