Math CentralQuandaries & Queries


Question from Kirstin, a student:
I am trying to take the limit of f(x) = [f(x+h)-f(x)] / h
If you try taking the limit by substituting the limiting value h=0, you get 0/0,
which of course is not the right answer. You rewrite f(x+h)-f(x) so it has a factor of h in it, which you cancel with the h in the denominator before you substitute h=0.
But I am not sure how to do this. Thanks.


You need to know what f is; in some cases it cannot even be done (these functions are called "nondifferentiable") and in other cases the math may be quite complicated.

If f is a polynomial it's straightforward algebra. If it's a trig function you may need to use some careful limit arguments.

If you are having difficulty with a particular function let us know.

Good Hunting


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