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lim(xrarr0) ((x+1)^(5)-1)/(x)...

`lim_(xrarr0) ((x+1)^(5)-1)/(x)`

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Verified by Experts

The correct Answer is:
5
`underset(xrarr0)"lim"((x+1)^(5)-1)/(x)`
`.^(5)C_(0)x^(5)+. ^(5)C_(1)x^(4)+.^(5)C_(2)x^(3)`
`underset(xrarr0)"lim"(+^(5)C_(3)x^(2)+^(5)C_(4)x+^(5)C_(5).1)/(x)`
`=underset(Xrarr0)"lim"((x^(5)+5x^(4)+10x^(3)+10x^(2)+5x+1)-1)/(x)`
`=underset(xrarr0)"lim"(x(x^(4)+5x^(3)+10x^(2)+10x+5))/(x)`
`=underset(xrarr0)"lim"(x^(4)+5x^(3)+10x^(2)+10x+5)
`=0+0+0+5=5`
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