Use Taylor series to evaluate the following limits. lim_{xrightarrow0}frac{sqrt{1+2x}-1-x}{x^2}

Maiclubk 2020-11-26 Answered
Use Taylor series to evaluate the following limits.
limx01+2x1xx2
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i1ziZ
Answered 2020-11-27 Author has 92 answers
Consider the given limit,
limx01+2x1xx2
use Taylor series expansion for the expression 1+2x
1+2x=(1+x12x2+12x358x4...)
Substitute the value into the limit,
limx01+2x1xx2=(1+x12x2+12x358x4...)1xx2
limx012x2+12x358x4...x2
limx012+12x58x2...
=12
hence the value of the limit is 12
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Jeffrey Jordon
Answered 2022-04-01 Author has 2087 answers

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