Limits and L'Hospital's Rule

L'Hospital's Rule 1 ${\textstyle \lim _{x\to 0}{f(x) \over g(x)}=lim_{x\to 0}{f'(x) \over g'(x)}}$ L'Hospital's Rule 2 Failed to parse (unknown function "\infinite"): {\textstyle \lim_{x\to \infinite } {f(x) \over g(x)} = lim_{x\to 0} {f'(x) \over g'(x)} }