Question

evaluate the limit
lim(x→49) (49 - x)/(7 - √x)

Explanation:

Step1: Rationalize the denominator

Multiply numerator and denominator by $7 + \sqrt{x}$.
\[

$$\begin{align*} \lim_{x ightarrow49}\frac{49 - x}{7-\sqrt{x}}\times\frac{7+\sqrt{x}}{7+\sqrt{x}}&=\lim_{x ightarrow49}\frac{(49 - x)(7+\sqrt{x})}{49 - x} \end{align*}$$

\]

Step2: Simplify the expression

Cancel out the common factor $49 - x$.
\[

$$\begin{align*} \lim_{x ightarrow49}\frac{(49 - x)(7+\sqrt{x})}{49 - x}&=\lim_{x ightarrow49}(7+\sqrt{x}) \end{align*}$$

\]

Step3: Evaluate the limit

Substitute $x = 49$ into $7+\sqrt{x}$.
\[
7+\sqrt{49}=7 + 7=14
\]

Answer:

$14$