Exercise 5.7

Question

Exercise 7: Suppose $f'(x)$, $g'(x)$ exist, $g'(x)
eq 0$, and $f(x)=f(x)=0$. Prove that $$\lim_{tightarrow x}\frac{f(t)}{g(t)}=\frac{f'(x)}{g'(x)}.$$

ghostofgarborg · Accepted Answer

(	extit{Matt ``Frito'' Lundy}) \
    We have:
    $$ \lim_{t 	o x} \frac{f(t)}{g(t)} 
    = \lim_{t 	o x} \frac{f(t) - f(x)}{t - x} \frac{t - x}{g(t) - g(x)} 
    = \frac {f'(x)}{g'(x)}$$

Exercise 5.7

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Exercise 5.7

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