`lim_(xto0)((x+1)^5-1)/(x)`

Options

A. `0`
B. `2`
C. `5`
D. इनमें से कोई नहीं

Answer

C

Explanation

`lim_(xto0)((x+1)^5-1)/(x)`
`= lim_(xto0)((.^(5)C_(0)x^(5)+.^(5)C_(1)x^4+.^(5)C_(2)x^3+.^(5)C_(3)x^2+.^(5)C_4x+.^(5)C_5.1)-1)/(x)`
`=lim_(xto0)((x^5+5x^4+10x^3+10x^3+10x^2+5x+1)-1)/(x)`
`=lim_(xto0)(x(x^4+5x^3+10x^2+10x+5))/(x)`
`= lim_(xto0)(x^4+5x^3+10x^2+10x+5)`
`=0+0+0+0+5=5`