Evaluate the following limit : lim(x→-1) (x^2 - x - 2)/((x^2+ x) + sin(x + 1))

Question

Evaluate the following limit : \(\lim\limits_{\text x \to-1}\cfrac{\text x^2-\text x-2}{(\text x^2+\text x)+sin(\text x+1)} \)

lim(x→-1) (x² - x - 2)/((x²+ x) + sin(x + 1))

Answer 1

We have \(\lim\limits_{\text x \to-1}\cfrac{\text x^2-\text x-2}{(\text x^2+\text x)+sin(\text x+1)} \)

Hence, \(\lim\limits_{\text x \to-1}\cfrac{\text x^2-\text x-2}{(\text x^2+\text x)+sin(\text x+1)} \) = ∞