select the correct answer.\nwhat is the left - hand limit of $g(x)=\frac{x^{2}-25}{x - 5}$ when $x$…
select the correct answer.\nwhat is the left - hand limit of $g(x)=\frac{x^{2}-25}{x - 5}$ when $x$ approaches 5?\na. 10\nb. 5\nc. 1\nd. 0
Answer
Answer:
A. 10
Explanation:
Step1: Factor the numerator
$x^{2}-25=(x + 5)(x - 5)$
Step2: Simplify the function
$g(x)=\frac{(x + 5)(x - 5)}{x - 5}=x + 5,x\neq5$
Step3: Find the left - hand limit
$\lim_{x\rightarrow5^{-}}g(x)=\lim_{x\rightarrow5^{-}}(x + 5)=5+5 = 10$