Question
Hi! How would you find the limit?
limit of (f(x+Δx)-f(x)) / Δ x with Δ x -> 0
f(x)= 3x-2
limit of (f(x+Δx)-f(x)) / Δ x with Δ x -> 0
f(x)= 3x-2
Answers
Darly
the Δx confuses me... How do I solve the problem when it has Δx?
Damon
this is the definition of the derivative
f(x+dx) = 3(x+dx)-2 = 3 x + 3 dx -2
f(x) = 3 x - 2
f(x+dx) - f(x) = 3 dx
divide by dx
= 3
f(x+dx) = 3(x+dx)-2 = 3 x + 3 dx -2
f(x) = 3 x - 2
f(x+dx) - f(x) = 3 dx
divide by dx
= 3
Damon
By the way since this particular function is linear, constant slope, there was no need for us to take the limit to find the derivative (slope at x is slope at any x)
Darly
OHH. THANK YOU SO MUCH!!
Damon
You are welcome.