If the function defined by f(x)= (1+x)^ 1+x x^2 - 1 x , x 0 is continuous at x=0 , then 6 f(0) is equal to

Step-by-step solution

We have, f(x)= (1+x)^ 1+x x^2 - 1 x aligned f(x) & = (1+x) (1+x) x^2 - 1 x & = (1+x) (1+x)-x x^2 aligned f(x) is continuous at x=0 aligned _ x 0 f(x) & =f(0) _ x 0 f(x) & = _ x 0 (1+x) (1+x)-x x^2 aligned Apply L-Hospital's rule aligned & _ x 0 (1+x) ( 1 1+x )+ (1+x)-1 2 x & _ x 0 (1+x) 2 x = 1 2 & f(0)= 1 2 & 6 f(0)=6 1 2 =3 aligned