Guess the value of the limit (correct to six decimal places). (if an answer does not exist, enter dne.) lim hâ0 (4 + h)5 â 1024 h

Recall the definition of the derivative of a function at a point :



We can then see that , and by the power rule we have . Then replacing , we arrive at



Alternatively, we could have expanded the binomial, giving





and so as we're left with 1280, as expected.