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If f(x)=(logx-log7)/(x^(2)-49) is contin...

If `f(x)=(logx-log7)/(x^(2)-49)` is continuous at x = 7, then f(7) is

A

`(1)/(7)`

B

`(1)/(49)`

C

`(1)/(98)`

D

`(1)/(79)`

Text Solution

Verified by Experts

The correct Answer is:
C
Given `f(x)=(log x-log7)/(x^(2)-49)`
Now, `lim_(x to 0)f(x)=lim_(x to 7) (logx-log 7)/(x^(2)-49)`
`=lim_(x to 7) ((1)/(x))/(2x) " " `[by L ' Hospital's rule]
`=(1)/(2xx7^(2))=(1)/(98)`
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