यदि `x=0` पर `f(x)=(x+1)^(cot x)` सतत है, तो `f(0)` किसके बराबर होगा ?

Options

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

Answer

A

Explanation

चूँकि फलन `f(x),x=0` पर सतत है ।

`:. underset(xrarr0)limf(x)=underset(xrarr0)lim(x+1)^(cot x)`

`= underset(xrarr0)lim[(1+x)^(1//x)]^(x cotx)`

` [ `चूंकि` underset(xrarr0)lim(1+x)^(1//x)=e]`

`=e^(underset(xrarr0)lim x cot x)=e^(underset(xrarr0)lim (x)/(tan x))`

`=e^(1)=e" "|`चूंकि` underset(xrarr 0)lim (x)/(tan x)=1`