L’Hôpital’s Rule

[smile4me8d21]

L’Hôpital’s Rule

Explain why L’Hôpital’s Rule cannot be used to find the limit of lim x->0 (e^2x)/x. Isn't it when it is undefined at 0 that L’Hôpital’s rule is used? I
am lost please help.

 

[pka]

Explain why L’Hôpital’s Rule cannot be used to find the limit of lim x->0 (e^2x)/x. Isn't it when it is undefined at 0 that L’Hôpital’s rule is used? I
am lost please help.

\(\displaystyle \displaystyle\lim_{x\to 0}x=0\)

\(\displaystyle \displaystyle\lim_{x\to 0}e^{2x}=1\ne 0\)

The rule does not apply! WHY?

 

[lookagain]

... find the limit of lim x->0 (e^2x)/x.

smile4me8d21,

what you typed is equivalent to this:


\(\displaystyle \displaystyle \lim_{x\to 0}\dfrac{e^2 x}{x}\)


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If you're going to type it out in a horizontal fashion, then use
grouping symbols as in:

lim x -> 0 of [e^(2x)]/x or of (e^(2x))/x.