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  • Find the value of   <img alt="\lim _{x \rightarrow a} \frac{x^2-a^2}{x-a}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Clim%20_%7Bx%20%5Crightarrow%20a%7D%20%5Cfrac%7Bx%5E2-a%5

Find the value of   \lim _{x \rightarrow a} \frac{x^2-a^2}{x-a}

Option: 1

2a


Option: 2

a


Option: 3

4a


Option: 4

4


Answers (1)

best_answer

Given,   \lim _{x \rightarrow a} \frac{x^2-a^2}{x-a}

By binomial theorem

\lim _{x \rightarrow a} \frac{x^n-a^n}{x-a}=n \cdot a^{n-1}

Here n=2

Then n \cdot a^{n-1}=2 \cdot a^{2-1}=2 a

 So, \lim _{x \rightarrow a} \frac{x^2-a^2}{x-a} = 2a

Posted by

Shailly goel

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