Question

lim deltax>0 (f(x+deltax)-f(x))/delta x find for f(x)=3x-2

Answer 1

x2+2xDeltaX+DeltaX2
x² + 2xΔx + (Δx)²
I'm going to use h instead of Δx.
x² + 2xh + h²

[x² + 2hx + h² - 2x - 2h + 1 - x² + 2x - 1] / h

Combining like terms:
[2hx + h² - 2h] / h

Divide out the h:
2x - 2 + h

Apply the limit
lim{h→0} [2x - 2 + h] = 2x - 2

Answer 2

why are you squaring? there is no square anywhere