Evaluate the following limit : lim(x→1)(x^3 + 3x^2-6x + 2)/(x^3 + 3x^2 - 3x - 1)

Question

Evaluate the following limit : \(\lim\limits_{\text x \to 1}\cfrac{\text x^3+3\text x^2-6\text x+2}{\text x^3+3\text x^2-3\text x-1} \)

lim(x→1)(x³ + 3x²- 6x + 2)/(x³ + 3x² - 3x - 1)

Answer 1

Since the form is

\(=\cfrac00\)

Method 1: factorization

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

Method 2: By L hospital rule:

Differentiating numerator and denominator separately: