L'Hopital's Rule Solution 3

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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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