question evaluate the limit: $lim_{x
ightarrow25}\frac{50 - 2x}{5-sqrt{x}}$

Question

Accepted Answer

# Answer:
$10$
# Explanation:
## Step1: Rationalize the denominator
Multiply numerator and denominator by $5 + \sqrt{x}$:
$$
\begin{align*}
\lim_{x
ightarrow25}\frac{50 - 2x}{5-\sqrt{x}}\times\frac{5+\sqrt{x}}{5+\sqrt{x}}&=\lim_{x
ightarrow25}\frac{(50 - 2x)(5+\sqrt{x})}{25 - x}\
\end{align*}
$$
## Step2: Factor out - 2 from the numerator
Factor $50 - 2x=-2(x - 25)$:
$$
\begin{align*}
\lim_{x
ightarrow25}\frac{-2(x - 25)(5+\sqrt{x})}{25 - x}&=\lim_{x
ightarrow25}\frac{-2(x - 25)(5+\sqrt{x})}{-(x - 25)}\
\end{align*}
$$
## Step3: Cancel out the common factor
Cancel out $(x - 25)$:
$$
\begin{align*}
\lim_{x
ightarrow25}\frac{-2(x - 25)(5+\sqrt{x})}{-(x - 25)}&=\lim_{x
ightarrow25}2(5+\sqrt{x})
\end{align*}
$$
## Step4: Substitute the value of x
Substitute $x = 25$:
$$
\begin{align*}
2(5+\sqrt{25})&=2(5 + 5)\
&=2\times10=10
\end{align*}
$$

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QUESTION IMAGE

Question

Explanation:

Step1: Rationalize the denominator

Step2: Factor out - 2 from the numerator

Step3: Cancel out the common factor

Step4: Substitute the value of x

Answer: