G

#### Guest

##### Guest

\(\displaystyle \lim_{x\to4}\ (3x+4)=16\)?

Can someone help me and explain it to me? I don't understand it.

G

\(\displaystyle \lim_{x\to4}\ (3x+4)=16\)?

Can someone help me and explain it to me? I don't understand it.

\(\displaystyle \lim_{dx\to0}\ (3(4+dx)+4)=16+e\)

12+3*dx+4=16+e

3*dx=e

as dx -> 0, e ->0

where dx is delta x and e is episilon.

If I'm wrong, (and no one else pops in) do you have an example from your book? It doesn't make much sense to me when you can just substitue x=4

G

I won't go into the theory behind it, but here's the procedure.How do you do an epislon delta proof for: \(\displaystyle \lim_{x\to4}\ (3x+4)=16\)?

Can someone help me and explain it to me? I don't understand it.

The epsilon statement is: .\(\displaystyle |(3x\,+\,4)\,-\,16|\,<\,\epsilon\) .

. . and we must manipulate it into the form: .\(\displaystyle |x\,-\,4|\,<\,\delta\) .

We have: .\(\displaystyle |3x\,-\,12|\,<\,\epsilon\)

Factor: . . \(\displaystyle |3(x\,-\,4)|\,<\,\epsilon\)

. . . . . . . . . \(\displaystyle 3|x\,-\,4|\,<\,\epsilon\)

. . . . . . . . . . \(\displaystyle |x\,-\,4|\,<\,\frac{\epsilon}{3}\)

We have