Question

details no additional details were added for this assignment. hw5 the limit laws (target l4; §2.3) score: 9/13 answered: 10/13 × question 10 score on last try: 0 of 1 pts. see details for more. > next question get a similar question you can retry this question below evaluate the limit lim (4 - a)/(2 - √a) as a→4

Explanation:

Step1: Rationalize the denominator

Multiply the numerator and denominator by the conjugate of the denominator $2 + \sqrt{a}$.
\[

$$\begin{align*} &\lim_{a ightarrow4}\frac{4 - a}{2-\sqrt{a}}\times\frac{2+\sqrt{a}}{2+\sqrt{a}}\\ =&\lim_{a ightarrow4}\frac{(4 - a)(2+\sqrt{a})}{4 - a} \end{align*}$$

\]

Step2: Simplify the expression

Cancel out the common factor $(4 - a)$ (since $a
eq4$ when taking the limit).
\[

$$\begin{align*} &\lim_{a ightarrow4}(2+\sqrt{a}) \end{align*}$$

\]

Step3: Evaluate the limit

Substitute $a = 4$ into the expression.
\[

$$\begin{align*} &2+\sqrt{4}=2 + 2=4 \end{align*}$$

\]

Answer:

$4$