How do you prove the statement lim as x approaches 4 for #(7 – 3x) = -5# using the epsilon and delta definition?
See the explanation section below.
Our preliminary work
We need to show that, given any positive
Let's look at the thing we need to make less than
# = abs(12-3x)#
Because we say how to find
Not that if we factor out a
# = abs(-3)abs(x-4) = 3abs(x-4)#
We have found that
If we make
Now we need to present ourwokr as a proof.
# = 3abs(x-4) < 3 delta = 3(epsilon/3) = epsilon.#.
near the middle we used, without mention, the fact that