Question

If f(x) = 3x^2 - 8x^-2, then lim as h approaches 0 f(2+h) - f(2) all over h =

Answer 1

Have you written out the question right?
Is it indeed "3x^2 -8x^-2" or "3x^2 - 8x - 2?"

Answer 2

its minus 8x to the negative 2

Answer 3

which is what made it so hard for me

Answer 4

I still don't quiet know what you're asking.

Answer 5

It's like using the derivative formula, kind of.... they want the limit and that is the equation

Answer 6

f(x) = 3x^2 - 8 x^-2
f(x+h) = 3(x+h)^2 - 8(x+h)^-2
f(x+h) = 3(x^2 + 2hx + h^2) - (8/(x^2+2hx+h^2) )
f(x+h) = 3x^2 + 6hx + 3h^2 - (8/x^2+2hx+h^2)

f'(x) = (f(x+h) - f(x))/h
f'(x) = (3x^2 + 6hx + 3h^2 - (8/x^2+2hx+h^2)) - (3x^2 - 8/x^2))/h
f'(x) = (6hx + 3h^2 +2hx+h^2)/h
f'(x) = h(6x + 3h+2x +h)/h
f'(x) = (6x +3h +2x+h)
f'(x) = lim h-> 0: 6x +2x


This is wrong and it's terrible to try and it's hard to follow when I am typing so I mess up or forget things easy, but just remember: 8x^-2 = 8/x^2

Hope it helps.