question 26 (1 point) find the limit algebraically. you must show work in order to receive credit! lim(x→4)…

Explanation:

Step1: Rationalize the denominator

Multiply numerator and denominator by $\sqrt{x}+2$. [ \begin{align*} &\lim_{x\rightarrow4}\frac{x - 4}{5(\sqrt{x}-2)}\times\frac{\sqrt{x}+2}{\sqrt{x}+2}\ =&\lim_{x\rightarrow4}\frac{(x - 4)(\sqrt{x}+2)}{5(x - 4)} \end{align*} ]

Step2: Simplify the expression

Cancel out the common factor $(x - 4)$. [ \begin{align*} &\lim_{x\rightarrow4}\frac{(x - 4)(\sqrt{x}+2)}{5(x - 4)}\ =&\lim_{x\rightarrow4}\frac{\sqrt{x}+2}{5} \end{align*} ]

Step3: Substitute $x = 4$

[ \begin{align*} &\frac{\sqrt{4}+2}{5}\ =&\frac{2 + 2}{5}\ =&\frac{4}{5} \end{align*} ]

Answer:

$\frac{4}{5}$