1) As we know,

D =

Therefore,

f(0.5) =

= 2.71766

2) As there are no loop in the graph of f(x)= provided below, and as the value of x approaches to zero from negative and positive side it does not shoot to any other value apart from the graph, thus the function is a continuous function.

ii) For a function to be differentiable if, = athen, = aTherefore, the above expression for 0 would become,

Expanding using Taylors series,

As we can see that,

The given function is differentiable.