details no additional details were added for this assignment. hw5 the limit laws (target l4; §2.3) score…

Explanation:

Step1: Rationalize the denominator

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

Step2: Simplify the expression

Cancel out the common factor $(4 - a)$ (since $a\neq4$ when taking the limit). [ \begin{align*} &\lim_{a\rightarrow4}(2+\sqrt{a}) \end{align*} ]

Step3: Evaluate the limit

Substitute $a = 4$ into the expression. [ \begin{align*} &2+\sqrt{4}=2 + 2=4 \end{align*} ]

Answer:

$4$