Limits doubt

[Shefali]

Q. (a^x-x^a)/(x^x-a^a)=-a
Find a.
 a 1
b 0
c e
d 1/e
e infinity

[mrittik]

kindly give da info abt limiting value plz

[Shefali]

Sorry limit is x tends to a.

[mrittik]

its a form of 0/0...so u can easily use the l'hospital rule here...now the limiting fn look like:

a^xlna-ax^(a-1)/(1+lnx)x^x=a^alna-a^a/(1+lna)a^a=lna-1/1+lna=-a=> 1-lna/1+lna=a

1-lna=a+alna=>1-a=(1+a)lna=> 2/(1+a)=lna...it comes like this..plz chk once

[Shefali]

Something like this bt i dont get answer.