Prove or disapprove f(x) is uniformly continuous

f(x)=(sinx)/x for x not equal to zero.

and f(x)=1 for x=0

I know f(x) is uniformly continous but I can't prove it. how do i show the derivative is bounded.

thanks

Printable View

- Mar 12th 2010, 07:41 AMcharikaarUniformly Continuous.
Prove or disapprove f(x) is uniformly continuous

f(x)=(sinx)/x for x not equal to zero.

and f(x)=1 for x=0

I know f(x) is uniformly continous but I can't prove it. how do i show the derivative is bounded.

thanks - Mar 12th 2010, 11:33 AM1234567
- Mar 12th 2010, 11:42 AMchisigma
Take into account that the coefficients of McLaurin expansion of of degree < 3 are equal to zero, so that is and that both the functions and tend to 0 if x tends to infinity...

Kind regards