Question

$\underset{x\to -2}{lim}\frac{x^3-7x-6}{x^4+5x-6}$

Answer 1

$y=\underset{x\to -2}{lim}\frac{x^3-7x-6}{x^{+}5x-6}$

using L'Hospital rule we have

$y=\underset{x\to -2}{lim}\frac{\frac{d}{dx}(x^3-7x-6)}{\frac{d}{dx}(x^4+5x-6)}=\frac{3x^2-7}{4x^3+5}$

Now put limit

$y=\frac{3(-2{)}^2-7}{4(-2{)}^3+5}=\frac{12-7}{-32+5}$

$[y=\frac{-5}{27}]$.