Here's the question you clicked on:
mathcalculus
HELP: use your knowledge of the derivative to compute the limit given below: lim (x+h)^(-3.25) -x^(-3.25)/h h->0 the derivative that is being calculated is dy/dx
That is just a complicated way of asking you: "What is the derivative of x^-3.25 ?"
oh.. but how do i get to my answer? what are the steps and why is it questioned in this format?
i know how to find the derivative ^
do we use quotient rule?
If you are allowed to "use your knowledge of the derivative", you could say that by definition the derivative of a function (here your function is x^-3.25) is the limit as h approaches 0 of f(x + h) - f(x). Therefore, this limit equals the derivative of x^-3.25 which is (and you know how to do the derivative, right?)
yes your derivative is correct
no quotient rule here
so whats the main purpose of these kinds of questions? for ex: what if it was a square root problem... do we find only the deriative of the f(x+h) an thats our answer?
find the derivative of f(x)...forget about the h. I think your prof just want's you to see how easy it is to do limits in that form now that you can do derivatives. Or maybe he / she wants to reinforce how derivatives relate to limits.
ex: (x+h)^(12/12) -x^(12/12) / h
so do we find the derivative: 12?