Evaluate the following limit : lim(x→√3) (x^4 - 9)/(x^2 + 4√3x - 15)

Question

Evaluate the following limit : \(\lim\limits_{\text x \to \sqrt3}\cfrac{\text x^4-9}{\text x^2+4\sqrt3\text x-15} \)

lim(x→√3) (x⁴ - 9)/(x² + 4√3x - 15)

Answer 1

Since the form is

\(=\cfrac00\)

Method 1: factorization

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

= 2

Method 2: By L hospital rule:

Differentiating numerator and denominator separately:

= 2