Let f: (0,1) --> R be any function with the following properties.

1)

2)

Then find:

I know that f(x) = sin(x^2) follows the above properties. Thus, . But I can't prove this for any general function.

Any hintss to get me started?

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- Nov 22nd 2011, 07:45 PMMy Little PonyFind the limit of the function with the given properties
Let f: (0,1) --> R be any function with the following properties.

1)

2)

Then find:

I know that f(x) = sin(x^2) follows the above properties. Thus, . But I can't prove this for any general function.

Any hintss to get me started? - Nov 23rd 2011, 12:19 AMchisigmaRe: Find the limit of the function with the given properties
- Nov 23rd 2011, 12:32 AMFernandoRevillaRe: Find the limit of the function with the given properties
- Nov 23rd 2011, 11:25 AMchisigmaRe: Find the limit of the function with the given properties
An alternative that doesn't require the derivative of f(x) starts setting . Now setting we have and the condition 2) becomes...

(1)

... and the only value of that satisfies (1) is ...

Kind regards