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Math Help - Show a function is continous

  1. #1
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    Show 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..

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  2. #2
    Member HappyJoe's Avatar
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    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.
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  3. #3
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    Thanks!
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  4. #4
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    You can also use a quick application of L'Hopital's rule.
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