(9am to 6pm)

Ask Questions, Get Answers

Want help in doing your homework? We will solve it for you. Click to know more.

If $\lim\limits_{x\to a}\large\frac{a^x-x^a}{x^x-a^a}$$=-1$ and $a > 0$ then $a$=?


1 Answer

Need homework help? Click here.
$\lim\limits_{\large x\to a}\large\frac{a^x-x^a}{x^x-a^a}\big(\large\frac{0}{0}\big)$
$\Rightarrow \lim\limits_{\large x\to a}\large\frac{a^x\log a-ax^{a-1}}{x(1+\log x)}$ (By L Hospital rule)
$\Rightarrow \large\frac{a^a\log a-a.a^{a-1}}{a^a(1+\log a)}$
$\Rightarrow \large\frac{a^a(\log a-1)}{a^a(1+\log a)}$
Hence (b) is the correct answer.
answered Jan 6, 2014 by sreemathi.v

Related questions