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Evaluate: ("lim")(xveca)((x+2)^(5/3)-(a+...

Evaluate: `("lim")_(xveca)((x+2)^(5/3)-(a+2)^(5/3))/(x-a)`

Text Solution

Verified by Experts

`underset(xtoa)lim((x+2)^(5//3)-(a+2)^(5//3))/(x-a)`
`=underset(xtoa)lim((x+2)^(5//3)-(a+2)^(5//3))/((x+2)-(a+2))`
`=underset(ytob)lim(y^(5//3)-b^(5//3))/(y-b),` where `x+2=y` and `a+2=b`
`=5/3b^(5//3-1)=5/3b^(2//3)=5/3(a+2)^(2//3)`
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