BG MATH HELP THREAD: Spring semester edition!

[Vandole]

i figured one of these bg math threads would pop up eventually and since i cant get this problem i'm working on right i figured someone here may be able to help me.

i'm working on a cal 1 epsilon delta proof that is

limit   (1/2x - 1)
x-> -4

here's my work so far

Spoiler: show

my teacher isnt going to test on this, yet he's requiring us to do these as a turnin for tomorrow. i would have made this thread earlier but i didn't have a book until about an hour ago(gogo poor college kid.)

[Demosthenes11]

just wait til you get to fucking complex assfuckery for delta epsilon

this shit is really important to learn though. don't really look for an answer as much as an understanding. if you understand, spatially, what this actually means, you have a very strong foundation to work on in calc. doesn't matter if they test on it

[Zounder]

^what he said, but here's the answer:

|((1/2)x-1)+3| < epsilon because it's really - -3.

Simplify that, factoring out a 1/2 leaves you with (1/2)|x+4|< epsilon
|x+4|< 2*epsilon, so let delta = 2*epsilon

[Mertron]

the answer is cows

[Vandole]

^what he said, but here's the answer:

|((1/2)x-1)+3| < epsilon because it's really - -3.

Simplify that, factoring out a 1/2 leaves you with (1/2)|x+4|< epsilon
|x+4|< 2*epsilon, so let delta = 2*epsilon

Thanks. I kept wanting to write that but for some reason i couldnt

[Cadsuane]

Yeah, this one is made intentionally easy. Remember though that the delta you choose is not a unique answer; for example any delta greater than 2 epsilon would also work in this example. Sometimes people get hung up on finding -the- delta when the point of the proof is to show that an arbitrary one can be found.

Also, a trick with inequalities:

0 < |x - c| < δ → -δ < x - c < δ

You can usually brute force the proof if you start like this.