Hay, TNL, Help Me with My Homework

I haven't gone home yet because I have literally one problem left on this assignment I want to hand in, and today's the last day I can hand it in.

I need to use the formal definition of a limit to prove (epsilon delta style) that the limit as x approaches 5 of sqrt(x) = sqrt(5).

So I start with |sqrt(x)-sqrt(5)| < epsilon, right?

And then I multiply by the conjugate to get |x-5|/(sqrt(x)+sqrt(5)).

And since sqrt(x)+sqrt(5) > sqrt(5) > 1, |x-5|/(sqrt(x)+sqrt(5)) < |x-5|, I think. delta is 1 in the above, I think...

But then what? ;_;

Someone help this man so he can get home to his family!

42?

I really wish math were taught differently. The easiest answer to the problem above to use one of 7,000 pieces of software to graph sqrt(x). We have a huge innumeracy issue, and the root cause is how many teachers have no fucking idea how to teach real world applications. Perhaps this is do to the old saying that those who can't do teach. I don't even remember what the hell the formal definition of a limit is, but I can sure as shit answer the question when I see the picture.

ok. I looked this up to refresh my memory.

|sqrt(x) - sqrt(5)| < epsilon is correct
that leads to
-epsilon < sqrt(x)-sqrt(5) < epsilon
-epsilon + sqrt(5) < sqrt(x) < epsilon + sqrt(5)
epsilon^2 - sqrt(5)*epsilon + 5 < x < epsilon^2 + sqrt(5)*epsilon + 5
epsilon^2 - sqrt(5) < x - 5< epsilon^2 + sqrt(5)*epsilon

Since we need gamma to be > 0 such that 0 < |x-a| < gamma, gamma would be epsilon^2 + sqrt(5)*epsilon, and you are done.

It's been a long time since I have had to do this (I took calculus in 1994), so please make sure I didn't do anything dumb.

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Originally Posted by Timber

42?

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lol.

Quote:

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Originally Posted by Yoshi

I really wish math were taught differently. The easiest answer to the problem above to use one of 7,000 pieces of software to graph sqrt(x). We have a huge innumeracy issue, and the root cause is how many teachers have no fucking idea how to teach real world applications. Perhaps this is do to the old saying that those who can't do teach. I don't even remember what the hell the formal definition of a limit is, but I can sure as shit answer the question when I see the picture.

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Personally, I think there is something fundamentally wrong with teaching math as if it was completely removed from the applications it was invented to solve. Like say how calculus was invented to do physics. It doesn't exist for its own sake, and yet it is taught that way.

But I guess it should be expected that I feel that way. I'm an engineer. Math is only a tool to me. I will never understand people who treat it as anything but a tool and make a living out of nitpicking the shit out of it.

I agree with you completely. I don't understand the math for the sake of math crowd. I also find statistics more interesting.

I love physics and hate math. Or rather, I love physics classes and hate math classes. So I agree with you guys.

After a bit more messing around with the route I was going, I think I'm good. You could definitely be right (not seeing anything wrong with it, myself), but he had a similar example of this recently that involved using the conjugate, and he's stupid nitpicky with this assignment, so I'm going to go with what I wound up with. Appreciated, though, Yoshi. Sorry about that.