# Chapter 4 - Applications of the Derivative - 4.7 L'Hopital's Rule - 4.7 Exercises - Page 307: 3

1) Verify $0/0$ form. 2) If 1) is verified apply equality $$\lim_{x\to a}\frac{f(x)}{g(x)}=\lim_{x\to a}\frac{f'(x)}{g'(x)}$$ 3) Calculate the limit. If the form is indeterminate again repeat from 1).

#### Work Step by Step

1) If given $$\lim_{x\to a}\frac{f(x)}{g(x)}$$ calculate $$\lim_{x\to a} f(x),\quad \lim_{x\to a}g(x).$$ if they are both equal to $0$ we got $0/0$ indeterminate form. 2) Apply equality $$\lim_{x\to a}\frac{f(x)}{g(x)}=\lim_{x\to a}\frac{f'(x)}{g'(x)}.$$ 3) Calculate $$\lim_{x\to a}f'(x),\quad \lim_{x\to a}g'(x)$$ if $\lim_{x\to a}f'(x)/\lim_{x\to a}g'(x)$ is determinate then the initial limit is equal to this ratio. If not repeat the procedure from step 1) but on the transformed limit.

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