lim-x-2-x-2-4-x-2-

Question Number 171247 by ilhamQ last updated on 11/Jun/22

\lim_{x \to 2} \frac{x^{2} - 4}{x - 2} = \dots

Answered by Rasheed.Sindhi last updated on 11/Jun/22

\lim_{x \to 2} \frac{x^{2} - 4}{x - 2} = ?

\begin{matrix} \lim_{x \to a} \frac{x^{n} - a^{n}}{x - a} = {n a}^{n - 1} \end{matrix}

\lim_{x \to 2} \frac{x^{2} - 4}{x - 2} = \lim_{x \to 2} \frac{x^{2} - 2^{2}}{x - 2} = 2 {(2)}^{2 - 1} = 4

[a = 2, n = 2]

Commented by peter frank last updated on 11/Jun/22

thank you

Answered by nurtani last updated on 11/Jun/22

\lim_{x \to 2} \frac{x^{2} - 4}{x - 2} = \lim_{x \to 2} \frac{(x - 2) (x + 2)}{(x - 2)}

= \lim_{x \to 2} (x + 2)

= 2 + 2

= 4

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