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Let f(x)=(g(x))/x w h e nx!=0 and f(0)=0...

Let `f(x)=(g(x))/x w h e nx!=0` and `f(0)=0.` If `g(0)=g^(prime)(0)=0a n dg^(0)=17` then `f(0)=` `3//4` b. `-1//2` c. `17//3` d. `17//2`

A

`3//4`

B

`-1//2`

C

`17//3`

D

`17//2`

Text Solution

Verified by Experts

The correct Answer is:
D
`f'(0)=underset(xrarr0)(lim)(f(x)-f(0))/(x-0)`
`=underset(xrarr0)(lim)(f(x))/(x)`
`=underset(xrarr0)(lim)(g(x))/(x^(2))`
`=underset(xrarr0)(lim)(g'(x))/(2x)`
`=(g''(0))/(2)=(17)/(2)`
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