Let f: R-->R be a differentiable function such that f(0)=f´(0)=0

Demonstrate that if lim f(x)/f´(x) exists, then that limit is equal to 0.

x→0

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- April 17th 2014, 03:23 PMYeisonCalculus
Let f: R-->R be a differentiable function such that f(0)=f´(0)=0

Demonstrate that if lim f(x)/f´(x) exists, then that limit is equal to 0.

x→0 - April 17th 2014, 03:24 PMYeisonRe: Calculus
I apologyze by not putting in an adequate form the limit when x tends to 0.

- April 17th 2014, 08:44 PMprasumRe: Calculus
here take newton raphsons form of soln

x(n+1)=x(n)-h(f(x(n))/f'(x(n)))

now take limit on both sides

lim(x(n+1)-x(n))=-hlim(f(x(n))/f'(x(n))) where x(n) -> 0

as we see the lhs limit is equal to 0 so for rhs either h=0 or the limit is equal to 0

but as we have taken h as some small value which is not equal to zero

therefore we have our rhs limit as zero