If `f(x)=(x+1)^(cotx)` is continuous at x=0, then what is f(0) equal to?

Options

A. 1
B. e
C. `(1)/(e)`
D. `e^(2)`

Explanation

For a function to be continuous at a point the limit should exist and should be equal to the value of the function at that point.
Here point is x=0
and `limf(x)=underset(xto0)lim(x+1)^(cotx)`
`=underset(xto0)lim(1+x)^(cotx)=underset(xto0)lim(1+x)^((1)/(x).cotx`
`=underset(xto0)lim(1+x)^((1)/xunderset(xto0)lim(x)/(tanx))=e^(1)=e`
Since limiting value of f(x)=e, when `xto0(0),f(0)` should also be equal to e.