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Find the value of n, if lim(xto2) (x^(n)...

Find the value of n, if `lim_(xto2) (x^(n)-2^(n))/(x-2)=80`, `n in N`.

A

`3`

B

`5`

C

`4`

D

`6`

Text Solution

Verified by Experts

The correct Answer is:
B
Given, `underset(xto2)"lim"(x^(n)-2^(n))/(x-2)=80`
`rArr n(2)^(n-1)=80` `[therefore underset(xtoa)"lim"(x^(n)-a^(n))/(x-a)=na^(n-1)]`
`rArr n(2)^(n-1)= 5 xx 16`
`rArr n xx 2^(n-1)= 5 xx (2)^(4)`
`rArr n xx 2^(n-1)= 5 xx (2)^(5-1)`
`therefore n=5`
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