it: $$ lim _ { x
ightarrow 121 } \frac { 121 - x } { 11 - sqrt { x } } $$

Question

Accepted Answer

# Explanation:
## Step1: Rationalize the denominator
Multiply numerator and denominator by $11 + \sqrt{x}$.
$$
\begin{align*}
&\lim_{x
ightarrow121}\frac{(121 - x)(11+\sqrt{x})}{(11-\sqrt{x})(11 + \sqrt{x})}\
\end{align*}
$$
Since $(a - b)(a + b)=a^{2}-b^{2}$, the denominator becomes $121 - x$.
## Step2: Simplify the expression
Cancel out the common factor $121 - x$ (for $x
eq121$).
$$
\begin{align*}
&\lim_{x
ightarrow121}\frac{(121 - x)(11+\sqrt{x})}{121 - x}\
=&\lim_{x
ightarrow121}(11+\sqrt{x})
\end{align*}
$$
## Step3: Substitute $x = 121$
$$
\begin{align*}
&11+\sqrt{121}\
=&11 + 11
\end{align*}
$$

# Answer:
$22$

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QUESTION IMAGE

Question

Explanation:

Step1: Rationalize the denominator

Step2: Simplify the expression

Step3: Substitute \(x = 121\)

Answer: