In this lesson, we will learn how to use the Lagrange error bound (Taylor’s theorem with remainder) to find the maximum error when using Taylor polynomial approximations.
Students will be able to
Q1:
Find the Lagrange error bound when using the second Taylor polynomial for the function π(π₯)=βπ₯ at π₯=4 to approximate the value β5. Round to five decimal places.
Q2:
Find the Lagrange error bound when using the third Maclaurin polynomial for the function π(π₯)=πο at π₯=0 to approximate the value πο±ο¦οο¨.
Q3:
Determine the least degree of the Maclaurin polynomials π needed to approximate the value of sin0.3 with an error less than 0.001 using the Maclaurin series of π(π₯)=π₯sin.
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