Question

What is L'hospital's Rule?

Answer 1

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.