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lim(xrarr1)(x^(m)-1)/(x^(n)-1) is equal ...

`lim_(xrarr1)(x^(m)-1)/(x^(n)-1)` is equal to

A

1

B

`m/n`

C

`-m/n`

D

`m^(2)/n^(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
Given, `lim_(xto1)(x^(m)-1)/(x^(n)-1) = lim_(xto1)((x^(m)-1)/(x-1))/((x^(n)-1)/(x-1))`
`(m(1)^(m-1))/(n(1)^(n-1)) = m/n` `[therefore (x^(n)-a^(n))/(x-a)=na^(n-1)]`
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