Using l'hopital's rule

Question:

!!lim_(x->2) (3^x + 3^(3-x) -12)/(3^(3-x)-3^x/2)!! x->2

  • !!(-2/3)!!
  • !!(2/3)!!
  • !!(-4/3)!!
  • !!(4/3)!!

Solution:

We can see that this function becomes !!(0/0)!! on putting the limit !!x=2!!.

So we can apply L'Hospital rule here and find the limit of the function.

!!lim_(x->2) (3^x + 3^(3-x) -12)/(3^(3-x)-3^x/2)!!

Applying L'Hospital's rule we get.

!!lim_(x->2)(3^xlog3-3^(3-x)log3)/(-3^(3-x)log3-(1/2)3^(x/2)log3)!!

!!lim_(x->2){3^x-3^(3-x)}/{3^(3-x)+(1/2)3^(x/2)}!!

!!=!! !!(-4/3)!!