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  4. If f(0) = 0 = g(0) and f'(0) = 6 = g'(0), then limx → 0 (f(x)/g(x)) is given by

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Q. If $f(0) = 0 = g(0) $ and $f'(0) = 6 = g'(0)$, then $\lim_{x \to 0} \frac{f(x)}{g(x)}$ is given by

Limits and Derivatives

Solution:

$\lim_{x \to0} \frac{f\left(x\right)}{g\left(x\right)} = \lim_{x \to0} \frac{f'\left(0\right)}{g'\left(0\right)} $ (By L’ Hospital rule)
$ = \frac{6}{6} = 1$