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underset(xrarr1)(lim)(root(13)x-root7x)/...

`underset(xrarr1)(lim)(root(13)x-root7x)/(root5x-root3x)` is

A

`(44)/(91)`

B

`(45)/(89)`

C

`(45)/(89)`

D

`(40)/(93)`

Text Solution

Verified by Experts

The correct Answer is:
B
`underset(xrarr1)(lim)(x^((1)/(13))-x^((1)/(7)))/(x^((1)/(5))-x^((1)/(3)))" "((0)/(0)"form")`
Apply L'Hospital's rule
`=underset(xrarr1)(lim)((1)/(13)x^(-1+(1)/(13))-(1)/(7)x^(-1+(1)/(7)))/((1)/(5)x^((1)/(5)-1)-(1)/(3)x^((1)/(3)-1))`
`=((1)/(13)-(1)/(7))/((1)/(5)-(1)/(3))=(45)/(91)`
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