Are the following true or false? A. When error term converges to 0 to Taylor ser

Question

Are the following true or false?

A. When error term converges to 0 to Taylor series represent the function

B. Same function can be represented with different power series through expansions at different points

C. Function may have multiple power series representation with the same point of expansion

D. Power series (as long as they represent the function) in the limit exactly coincide with the function, however partial sums only approximate a function. Apprixomation is best near the point of expansion

Explanation / Answer

Following is the answers of above questions.

A. True

B.Yes (if the point of expansion is different then the series will be different)

C.False (if point of expansion is same then then there will be single power series)

D.True

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