Question

limit of (((x-5)^2)-25))/(x) as x approaches 0.
I need the steps on how to solve it.

Answer 1

\(\lim\limits_{x \to 0} \dfrac{(x-5)^2-25}{x }\)

\(= \lim\limits_{x \to 0} \dfrac{(x^2 - 10 x + 25)-25}{x }\)

\(= \lim\limits_{x \to 0} \dfrac{x(x - 10 )}{x }\)


\(= \lim\limits_{x \to 0} (x - 10 ) = - 10\)