Find the limit.
-$\lim _ { x \rightarrow 5 } \sqrt { x ^ { 2 } + 10 x + 25 }$
A) ±10
B) 10
C) 100
D) does not exist

Question

Quizplus · Accepted Answer

We can simplify the expression inside the square root by recognizing that it is equal to $(x+5)^2$. Therefore, the original limit is equivalent to:
$$\lim_{x\rightarrow 5} \sqrt{(x+5)^2} = \lim_{x\rightarrow 5} |x+5| = |5+5| = 10$$
Since the limit exists and is equal to 10, the answer is B.

Find the Limit lim⁡x→5x2+10x+25\lim _ { x \rightarrow 5 } \sqrt { x ^ { 2 } + 10 x + 25 }limx→5​x2+10x+25​

Find the Limit $\lim _ { x \rightarrow 5 } \sqrt { x ^ { 2 } + 10 x + 25 }$