Question

Find all possible value of $a$, if $\underset{x\to a}{lim}{\left(\frac{x^9-a^9}{x-9}\right)}^x=\underset{x\to 3}{lim}(6+x)$

• A. $6$
• B. $0$
• C. $9$
• D. $16$

Answer 1

The correct option is C $9$

Given: ${lim}_{x\to a}{\left(\frac{x^9-a^9}{x-9}\right)}^x={lim}_{x\to 3}(6+x)$

To find: All possible values of a

Sol: ${lim}_{x\to a}{\left(\frac{x^9-a^9}{x-9}\right)}^x={lim}_{x\to 3}(6+x)$

For limit to exist, it will have to have some uncertainity

$⟹{lim}_{x\to a}\left(\frac{x^9-a^9}{x-9}\right)=\frac{a^9-a^9}{a-9}$

Possible if a=9

Hence a=9