Answer:
[tex]= \dfrac{1}{75}[/tex]
Step-by-step explanation:
Given that:
[tex]\lim_{x \to -5} \dfrac{(x+5)}{(x^3+125)}[/tex]
[tex](x^3 + 125) = (x+5)(x^2 -5x+25)[/tex]
Thus;
[tex]= \lim_{x \to -5} \dfrac{(x+5)}{(x+5)(x^2 -5x +25)}[/tex]
[tex]= \lim_{x \to -5} \dfrac{1}{(x^2 -5x +25)}[/tex]
[tex]= \dfrac{1}{((-5)^2 -5(-5) +25)}[/tex]
[tex]= \dfrac{1}{(25 +25 +25)}[/tex]
[tex]= \dfrac{1}{75}[/tex]
