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
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.