Answer: = 8x - 5
Explanation:
f(x) = 4x² - 5x
Find:
lim as Δx⇒0 [f(x + Δx) - f(x)] /Δx
This is the same as finding the derivative. For f(x + Δx) means substitute x + Δx into the function everytime you see an x.
Solution:
lim as Δx⇒0 [f(x + Δx) - f(x)] /Δx
lim as Δx⇒0 [4(x + Δx)² - 5(x + Δx) - (4x² - 5x)] /Δx >Simplify
lim as Δx⇒0 [4(x²+2x(Δx) +(Δx)²) - 5x- 5Δx - 4x²+ 5x] /Δx
lim as Δx⇒0 [4x²+8x(Δx) +4(Δx)² - 5x- 5Δx - 4x²+ 5x] /Δx
lim as Δx⇒0 [8x(Δx) +4(Δx)²- 5Δx] /Δx >Divide by Δx
lim as Δx⇒0 8x +4(Δx)- 5 >set Δx to 0 because it is approaches
= 8x - 5
You can check this using the power rule and take derivative of f(x) and it checks out.