Question

 If 'f' is continuous at x = 0, then find f(0).

`f(x)=(15^x-3^x-5^x+1)/(xtanx) , x!=0`

Answer 1

`f(x)=(15^x-3^x-5^x+1)/(xtanx) , x!=0`

`lim_(x->0)f(x)=lim_(x->0)(15^x-3^x-5^x+1)/(xtanx)  `

`=lim_(x->0)(3^x(5^x-1)-(5^x-1))/(xtanx) `

`=lim_(x->0)((3^x-1)(5^x-1))/(xtanx)`

`=lim_(x->0)([(5^x-1)/x][(3^x-1)/x])/ ((xtanx/x^2))                                                                                                  `

`=(log5.log3)/1                     `

`=log5.log3`

As function is continuous at x=0

`f(0)=lim_(x->0)f(x)`

f(0)=log5.log3