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If lim(xto2) (x^(n)-2^(n))/(x-2)=80" and...

If `lim_(xto2) (x^(n)-2^(n))/(x-2)=80" and " ninN, " then find the value of n."`

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Verified by Experts

We have `underset(xto2)lim(x^(n)-2^(n))/(x-2)=80`
or `" "n2^(n-1)=80`
or `" "n2^(n-1)=5xx2^(5-1)`
or `" "n=5`
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