Question

Evaluate the Given limit: \(\lim_{x\rightarrow 2}\) \(\frac{3x^2-x-10}{x^2-4}\)

Answer 1

At x = 2, the value of the given rational function takes the form 0/0
\(\lim_{x\rightarrow 2}\) \(\frac{3x^2-x-10}{x^2-4}\) =\(\lim_{x\rightarrow 2}\) \(\frac{(x-2)(3x+5)}{(x-2)(x+2)}\)
\(\lim_{x\rightarrow 2}\) \(\frac{3x+5}{x+2}\)
=\(\frac{3(2)+5}{2+2}\)
=\(\frac{11}{4}\)