what is the limit? lim x→5 (√(x + 4) - 3)/(x - 5) 0 dne 1/6 -1/6

Explanation:

Step1: Rationalize the numerator

Multiply by $\frac{\sqrt{x + 4}+3}{\sqrt{x + 4}+3}$. $\lim_{x\rightarrow5}\frac{\sqrt{x + 4}-3}{x - 5}\times\frac{\sqrt{x + 4}+3}{\sqrt{x + 4}+3}=\lim_{x\rightarrow5}\frac{(x + 4)-9}{(x - 5)(\sqrt{x + 4}+3)}$

Step2: Simplify the numerator

$(x + 4)-9=x - 5$. $\lim_{x\rightarrow5}\frac{x - 5}{(x - 5)(\sqrt{x + 4}+3)}$

Step3: Cancel out common factors

Cancel out $x - 5$. $\lim_{x\rightarrow5}\frac{1}{\sqrt{x + 4}+3}$

Step4: Substitute $x = 5$

$\frac{1}{\sqrt{5+4}+3}=\frac{1}{3 + 3}=\frac{1}{6}$

Answer:

C. $\frac{1}{6}$