Evaluate the limit, if it exists. (if an answer does not exist, enter dne.)lim h → 0 (x + h)3 − x3h

Presumably, the limit is



Now, if you're familiar with the definition of the derivatives, you'll notice that this is the limit form of the derivative of the function , which you may also know to be . But let's assume you don't know that just yet, and that it's actually the result you intend to find.

Expand the numerator:



Now, when , we can divide through by the lowest power of . We can do this because we're considering the limit as is *approaching* 0, and not when it actually takes on the value of .



Now, as , we can see only the leading term remains, so that



as expected.