Home » Blog » Evaluate the limit

Evaluate the limit


    \[ \lim_{a \to 0} \frac{x^2 - a^2}{x^2 + 2ax + a^2}, \qquad \text{for } x \neq 0. \]

Since the numerator and denominator are both polynomials, they are continuous. Since the denominator is non-zero for x \neq 0, we may apply Theorem 3.2 to conclude f/g is continuous. So, we can compute the limit,

    \[ \lim_{a \to 0} \frac{x^2-a^2}{x^2 + 2ax + a^2} = \frac{x^2}{x^2} = 1. \]

Point out an error, ask a question, offer an alternative solution (to use Latex type [latexpage] at the top of your comment):