`lim_(x rarr 0) ((1+x)^(n)-1)/(x)` किसके तुल्य है ?

Options

A. 0
B. 1
C. n
D. n-1

Answer

C

Explanation

`underset(xrarr0)lim{((1+x)^(n)-1)/(x)}`
`=underset(xrarr0)lim((1+nx+(n(n-1))/(2!)x^(2)+...)-1)/(x)` [द्विपद प्रमेय (कोई घातांक )से ]
`=underset(xrarr0)lim(nx+(n(n-1))/(2!)x^(2)+...)/(x)`
`=underset(xrarr0)limn+(n(n-1))/(2!)x+...`
`=n+0+0+...=n`