L’Hospital Rule states that

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a) If \(\lim_{x\rightarrow a}\frac{f(x)}{g(x)}\) is an indeterminate form than \(\lim_{x\rightarrow a}\frac{f(x)}{g(x)}=\lim_{x\rightarrow a}\frac{f'(x)}{g'(x)}\) if \(\lim_{x\rightarrow a} \frac{f'(x)}{g'(x)}\) has a finite value
b) \(\lim_{x\rightarrow a}\frac{f(x)}{g(x)}\) always equals to \(\lim_{x\rightarrow a}\frac{f'(x)}{g'(x)}\)
c) \(\lim_{x\rightarrow a}\frac{f(x)}{g(x)}\) if an indeterminate form than cannot be solved
d) \(\lim_{x\rightarrow a}\frac{f(x)}{g(x)}\) if an indeterminate form than it is equals to zero.