Biology Forums - Study Force

Can someone confirm if these answers are correct? Thanks
a) y = 8x
lim h->0 f(x + h) - f(x)/h
lim h->0 8(x + h) - 8x/h <- Distribute the 8(x +h)
lim h->0 8x + 8h - 8x/h <- Cancel out 8x and -8x
lim h->0 8h/h <- Cancel h's
lim h->0 = 8

b) 3x^2 - 2x
lim h->0 f(x + h) - f(x)/h
lim h->0 3(x + h)^2 - 2(x + h) - (3x^2 - 2x)/h <- Distribute -2(x + h) and -(3x^2 - 2x)
lim h-> 3x^2 + 6xh + 3h^2 - 2x - 2h - 3x^2 + 2x/h <- Cancel out
lim h->0 3h^2 + 6xh - 2h/h = h(3h + 6x - 2)/h <- Cancel out
lim h->0 3h + 6x - 2
lim h->0 dy/dx = 6x - 2

c) (2x - 1)^2 -> (2x - 1)(2x - 1) = 4x^2 - 4x +1
lim h-> 0 f(x + h) - f(x)/h
lim h->0 4(x + h)^2 - 4(x + h) + 1 - (4x^2 - 4x + 1)/h <- Distribute
lim h->0 4x^2 + 8xh + 4h^2 - 4x - 4h + 1 - 4x^2 + 4x - 1/h
lim h->0 4h^2 + 8xh - 4h/h = 4h(h + 2x -1)/h ,- Cancel out + Distribute the 4
= dy/dx 8x-4

All of these are correct 👍 👍