Lecture 13: Taylor and Maclaurin Series - NU Math Sites
One application of Taylor series is to justify the use of L`H^opital's Rule. Example. Find the limit lim x ! 0 sin( x ) x. We could evaluate the limit with L`H^opital's Rule, but let's use the Maclaurin series instead. lim x ! 0 sin( x ) x = lim x ! 0 x x 3 3! + x 5 5! x 7 7! + x = lim x ! 0 1 x 2 3! + x 4 5! x 6 7! + = 1 : The result agrees ... ................
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