Evaluate the following limit. lim_{xrightarrow0^+}(1+5x)^{2/x}

nagasenaz 2020-11-30 Answered
Evaluate the following limit.
limx0+(1+5x)2/x
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Expert Answer

okomgcae
Answered 2020-12-01 Author has 93 answers
Evaluate limits:
limx0+(1+5x)2/x
Apply exponent rule:
ax=eln(ax)=exln(a)
(1+5x)2x=e2xln(1+5x)
Apply the Limit Chain Rule:
g(x)=2xln(1+5x),f(u)=eu
limx0+g(x)=limx0+2xln(1+5x)
=2limx0+(ln(1+5x)x)
limx0+(ln(1+5x)x)=00
LHospital
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