L'Hopital's Rule Solution 2

SOLUTION 2: $$ \displaystyle{ \lim_{x \rightarrow 4} \frac{ x-4 }{ \sqrt{x}-2 } } = \displaystyle{ \frac{ (4)-4 }{ \sqrt{4}-2 } } = \frac{"0"}{0} $$
(Apply Theorem 1 for l'Hopital's Rule. Differentiate top and bottom separately.)
$$ = \displaystyle{ \lim_{x \rightarrow 4} \frac{ 1-0 }{ 1/2\sqrt{x}-0 } } $$ $$ = \displaystyle{ \lim_{x \rightarrow 4} 2\sqrt{x} } $$ $$ = \displaystyle{ 2 \sqrt{4} } $$ $$ = \displaystyle{ 2 (2) } $$ $$ = \displaystyle{ 4 } $$

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