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Lecture

11.10 Taylor & Maclaurin Series Question #2 (Medium)

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Department
Mathematics
Course
MAT136H1
Professor
All Professors
Semester
Winter

Description
11.10 Infinite Sequences & Series Taylor & Maclaurin Series Question #2 (Medium): Taylor Series and Its Radius of Convergence Strategy ( ( ) ( ) ( ) Taylor series states: ( ) ∑ ( ) ( ) ( ) ( ) ( ) ( ) Radius of convergence is determined using the ratio test | | So any value of that makes the limit to be less than falls in the radius of convergence. Sample Question Find the Taylor series for ( ) centered at the given value of . Assume that f has a power series expansion. Do not show that Also find the associated radius of convergence. ( ) , Solution Taylor series requires derivative in sequential order. Thus, for , use the function as it is, so ( ) ; for , its first derivative, matching with the number , so: ( ) ; for , second derivative: ( ) ; for , third derivative: ( )( ) ; for , fourth
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