Prove lim_(xrarr5)(2x+4)=14?

1 Answer
Aug 8, 2018

We can prove this in a number of ways. Since this is classified as pre-calculus, I will avoid an epsilon - delta proof.

In general, a limit is the value that a function approaches. Let
f(x) = 2x+4.

First, let's just justify it numerically.

If we plug in values just barely less than x=5, we see that the values approach 14, i.e.
f(4) = 12
f(4.9) = 13.8
f(4.99) = 13.98
f(4.999) = 13.998
and so on and so forth

The same applies if we plug in values just barely above x=4:
f(6) = 16
f(5.1) = 14.2
f(5.01) = 14.02
f(5.001) = 14.002

This means that as x rightarrow 5, the function approaches 14.

Now, we can also sort of prove this limit:

For a function that is "simple", such as this line, we can actually just plug in the value and get our answer, too.

f(5) = 2 * 5 + 4 = 14