Question

Let f(x)=7/(x-6). Then according to the definition of derivative:

f'(x) = lim x->t (FILL IN THE BLANK)


Help please!!

Answer 1

I know the formula for the limit definition: [f(x+h) - f(x)]/h. But when I plug it in with the given function, the computer tells me that it's wrong

Answer 2

\[
f'(t) = \lim_{x\to t}\frac{f(x)-f(t)}{x-t}
\]

Answer 3

Ohh you're using that formula. So I just plug in t for x?

Answer 4

well, if you let \(x\to t\) then \(x\) is a dummy variable so you can't really use as an input for the derivative.

Answer 5

It is was \(t\to x\) then you would have \(f'(x)\) instead of \(f'(t)\)

Answer 6

i meant t->x sorry!

Answer 7

The dummy variable of your limit can't be recycled as the input variable for the function.

Answer 8

Normally the dummy variable would be \(h\) or \(a\) or \(\Delta x\), but not \(x\) itself.

Answer 9

Ok. It says I got it right now. Thanks for the help!!