Im not sure how to do this question because it is slightly different (there isnt a term like x^2 - 5x +2 etc.. but this is just h(x) and f(x). Thanks..

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- May 12th 2011, 04:41 AMqwerty1234Show a function is continous
Im not sure how to do this question because it is slightly different (there isnt a term like x^2 - 5x +2 etc.. but this is just h(x) and f(x). Thanks..

ImageShack® - Online Photo and Video Hosting - May 12th 2011, 05:24 AMHappyJoe
The only point at which we can be in doubt that h is continuous is at x=0. To prove that h is continuous at this point, you need to check that f(x)/x tends to f'(0) as x->0. Is this true?

To find out, consider how f'(0) is defined, i.e. f'(0) is the limit of some quotient, which might turn out to resemble f(x)/x. - May 12th 2011, 11:50 AMqwerty1234
Thanks!

- May 12th 2011, 12:38 PMDrSteve
You can also use a quick application of L'Hopital's rule.