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Lecture

11.10 Taylor & Maclaurin Series Question #1 (Easy)

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Department
Mathematics
Course
MAT136H1
Professor
All Professors
Semester
Winter

Description
11.10 Infinite Sequences & Series Taylor & Maclaurin Series Question #1 (Easy): Maclaurin Series and Radius of Convergence Strategy Maclaurin series is exactly same as Taylor series of the function at , but where ( ) ( ) ∑ ( ) ( ) ( ) ( ) ( ) Sample Question Find the Maclaurin series for ( ) using the definition of Maclaurin series. Assume that has a power series expansion. Do not show that Also find the associated radius of convergence. ( ) ( ) Solution Since Maclaurin series requires derivative of the given function, ( ) ( ) which is the first term for . For : ( ) ( ) ( ) Likewise for : ( ) ( )( ) ( ) ( ) For : ( ) ( )( ) ( ) For : ( ( ) ( )( )
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