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If f(x)=sqrt(x^(2)+9)," then "lim(xto4) ...

If `f(x)=sqrt(x^(2)+9)," then "lim_(xto4) (f(x)-f(4))/(x-4)` has the value

A

`5//4`

B

`-4//5`

C

`4//5`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
We have,
`f(x)=sqrt(x^(2)+9)`
`implies" "f'(x)=(x)/(sqrt(x^(2)+9))`
Now,
`underset(xto4)lim(f(x)-f(4))/(x-4)=f'(4)" "["By def. of derivative"]`
`implies" "underset(xto4)lim(f(x)-f(4))/(x-4)=(4)/(sqrt(4^(2)+9))=(4)/(5)`
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