First, be aware that I not really sure that I understand you difficulty here.
That said, surely it is clear to you that this is true:
Now tell us what you don't understand.
Hi, everyone! I have a minor problem proving the two following definitions of the derivative are equivalent:
f is differentiable iff exists
and
f is differentiable iff exists.
I know that i can let , so that and , but then how can i explain the limits part, when in first case i am taking limit as x approaches and in second as t approaches 0?
Thanks in advance!
Yea, i'm aware of that, but i'm not sure how I can apply that knowledge to my problem, since as far as I am concerned i'm not taking limit of t as t goes to 0, but rather limit of difference quotient as t goes to 0, where difference quotient need not be t. I guess what I really wanted to know is whether is generally true for any . Correct me if i'm totally off the track.