Question

Assumptions:

The formal definition of the limit of a function is as follows: Let ƒ : D →R with x₀ being an accumulation point of D. Then ƒ has a limit L at x₀ if for each ∈ > 0 there is a δ > 0 that if 0 < |x – x₀| < δ and x ∈ D, then |ƒ(x) – L| < ∈.

Let L = 4P + Q. when P = 6 and Q = 24

Define your function to be f(x) = Px + Q where f(x) is a function from the real numbers to the real numbers.

A. Compute a δ that is appropriate to prove your function, f(x), converges to L. Show your work.

1. For ε > 0, prove that   x→4   lim f (x) = L by using the formal definition of a limit of the function in the Assumptions section. Show and justify your work.

Answer 1