Evaluate the following limits: lim(x→-1)(x^3 + 1)/(x + 1)

Question

Evaluate the following limits: \(\lim\limits_{\text x \to-1}\cfrac{\text x^3+1}{\text x+1} \)

lim(x→-1)(x³ + 1)/(x + 1)

Answer 1

Since the form is indeterminant

\(=\cfrac00\)

Method 1: factorization

Since a³ + b³ = (a + b)(a² + b² - ab) & a² - b² = (a + b) (a - b)

= (-1)² + (1)² - (-1)

= 3

Method 2 : By L hospital rule:

Differentiating numerator and denominator separately:

= 3(-1)²

= 3