L'Hopital's Rule Solution 3

SOLUTION 3: $$ \displaystyle{ \lim_{x \rightarrow 0} \frac{ \sin x }{ x } } = \displaystyle{ \frac{ \sin(0) }{ 0 } } = \frac{"0"}{0} $$
(Apply Theorem 1 for l'Hopital's Rule. Differentiate top and bottom separately.)
$$ = \displaystyle{ \lim_{x \rightarrow 0} \frac{ \cos x }{ 1 } } $$ $$ = \displaystyle{ \cos(0) } $$ $$ = \displaystyle{ 1 } $$

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