Question

The value of $\lim_{𝑥→−3}\frac{(2𝑥+6)}{(𝑥+3)}$ is

Answer 1

Correct Answer: 2

To find the limit $\lim_{x \to -3} \frac{2x+6}{x+3}$, we begin by substituting $x = -3$ into the expression. Direct substitution yields:

$\frac{2(-3) + 6}{-3 + 3} = \frac{-6 + 6}{0} = \frac{0}{0}$

This is an indeterminate form, so we need to simplify the expression. Notice that:

$2x + 6 = 2(x + 3)$

Thus, the expression becomes: 

$\frac{2(x+3)}{x+3}$

If $x \neq -3$, we can cancel $(x+3)$:

$= 2$

Since the simplification holds for all $x \neq -3$, the limit is:

$\lim_{x \to -3} \frac{2(x+3)}{x+3} = 2$

This result, $2$, falls within the given range of 2,2, confirming its validity.