Use Taylor series to evaluate the following limits. lim_{xrightarrow4}frac{ln(x-3)}{x^2-16}

texelaare 2020-11-22 Answered
Use Taylor series to evaluate the following limits.
limx4ln(x3)x216
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Expert Answer

Cullen
Answered 2020-11-23 Author has 89 answers
To evaluate the limit using Taylor series,
limx4ln(x3)x216
ln(1+x)=xx22+x33x44+...
ln(x3)=ln(1+(x4))
=(x4)(x4)22+(x4)33(x4)44+...
limx4ln(x4)x216=(x4)(x4)22+(x4)33(x4)44+...(x4)(x+4)
=(x4)[1(x4)2+(x4)23(x4)34+...](x4)(x+4)
1(x4)2+(x4)23(x4)34+...x+4
10+00+...4+4
=18
limx4ln(x3)x216=18
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Jeffrey Jordon
Answered 2022-04-01 Author has 2047 answers

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