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Evaluate lim(xrarra)((x^(m)-a^(m))/(x^(n...

Evaluate `lim_(xrarra)((x^(m)-a^(m))/(x^(n)-a^(n))).`

Text Solution

Verified by Experts

`lim_(xtoa)((x^(m)-a^(m))/(x^(n)-a^(n)))=lim_(xtoa){((x^(m)-a^(m))/(x-a))div((x^(n)-a^(n))/(x-a))}`
`=lim_(xtoa)((x^(m)-a^(m))/(x-a))divlim_(xtoa)((x^(n)-a^(2))/(x-a))`
`=(ma^(m-1))(na^(n-1))`
`=(ma^(m-1))/(na^(n-1))=m/na^(m-n).`
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