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Evalvate lim(xrarr0)((1+x)^(4)-1)/(x)....

Evalvate `lim_(xrarr0)((1+x)^(4)-1)/(x).`

Text Solution

Verified by Experts

Put `(1+x)=y,` so that when `xto 0 then y to 1.`
`thereforelim_(xto0)((1+x)^(4)-1)/(x)=lim_(y to1)((y^(4)-1)/(y-1))=lim_(y to1)((y^(4)-1^(4))/(y-1))`
`=4xx1^((4-1))" "[becauselim_(xtoa)((x^(n)-a^(n))/(x-a))=na^(n-1)]`
`=(4xx1^(3))=4.`
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