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

$$\underset{x\to 2}{\lim }\frac{x^2-4}{x-2}=...$$

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

$$\underset{x\to 2}{\lim }\frac{x^2-4}{x-2}=?$$$$\overline{)\begin{array}{c}\underset{x\to a}{\lim }\frac{x^n-a^n}{x-a}={na}^{n-1}\end{array}}$$$$\underset{x\to 2}{\lim }\frac{x^2-4}{x-2}=\underset{x\to 2}{\lim }\frac{x^2-2^2}{x-2}=2{\left(2\right)}^{2-1}=4$$$$[a=2,n=2]$$

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

$$\mathrm{thank}\mathrm{you}$$$$$$

Answered by nurtani last updated on 11/Jun/22

$$\underset{x\to 2}{\lim }\frac{x^2-4}{x-2}=\underset{x\to 2}{\lim }\frac{\cancel{(x-2)}(x+2)}{\cancel{(x-2)}}$$$$=\underset{x\to 2}{\lim }(x+2)$$$$=2+2$$$$=4$$

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