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If f(x)=sqrt(x^2+9) , write the value of...

If `f(x)=sqrt(x^2+9)` , write the value of `(lim)_(x->4)(f(x)-f(4))/(x-4)` .

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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Knowledge Check

  • If f(x)=(sqrt(x^(2)-4))/(x-4) , what are all the values of x for which f(x) is defined ?

    A
    All real numbers except 4
    B
    All real numbers except - 2 and 2
    C
    All real numbers greater than or equal to -2 and less than or equal to 2
    D
    All real numbers less than or equal to -2 or greater than or equal to 2, except 4

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