Evaluate the following limits: lim(x→5) (x^2-9x + 20)/(x^2 - 6x + 5)

Question

Evaluate the following limits: \(\lim\limits_{\text x \to 5}\cfrac{\text x^2-9\text x+20}{\text x^2-6\text x+5} \)

lim(x→5) (x²- 9x + 20)/(x² - 6x + 5)

Answer 1

Since the form is indeterminant

\(=\cfrac00\)

Method 1: factorization

Method 2:

By L hospital rule:

Differentiating numerator and denominator separately: