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

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- March 12th 2010, 08:41 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 - March 12th 2010, 12:33 PM1234567
- March 12th 2010, 12:42 PMchisigma
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