Question

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

Answer 1

That is just a complicated way of asking you:
"What is the derivative of x^-3.25 ?"

Answer 2

oh.. but how do i get to my answer? what are the steps and why is it questioned in this format?

Answer 3

i know how to find the derivative ^

Answer 4

-3.25x^-4.25

Answer 5

do we use quotient rule?

Answer 6

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?)

Answer 7

yes your derivative is correct

Answer 8

no quotient rule here

Answer 9

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?

Answer 10

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.

Answer 11

ex: (x+h)^(12/12) -x^(12/12) / h

Answer 12

so do we find the derivative: 12?