What is L'hospital's Rule?

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Answer 1 · 2014-09-28T14:18:26

l'Hopital's Rule

If #{(lim_{x to a}f(x)=0 and lim_{x to a}g(x)=0), (or), (lim_{x to a}f(x)=pm infty and lim_{x to a}g(x)=pm infty):}#

then

#lim_{x to a}{f(x)}/{g(x)}=lim_{x to a}{f'(x)}/{g'(x)}#.

Example 1 (0/0)

#lim_{x to 0}{sinx}/x=lim_{x to 0}{cosx}/1={cos(0)}/1=1/1=1#

Example 2 (#infty#/#infty#)

#lim_{x to infty}{x}/{e^x}=lim_{infty}{1}/{e^x}=1/{e^{infty}}={1}/{infty}=0#

I hope that this was helpful.