Question

calculus - let f(x)={0, if x is rational and {1, if x is irrational; and let g(x)={0 if x is rational and {x if x is irrational. Find (if possible) lim X->0, f(x) and g(x)

Answer 1

Limit for f is undefined, limit for g is 0. The reason becomes clear when you start thinking about the epsilons and deltas. For f, you're never going to be able to find an appropriate delta, because there will always be another irrational number bringing the value back up to 1. For g, you will be able to, because it's x at x. Sorry if that's a bad explanation, having a hard time putting it into words.

Answer 2

By undefined I mean limit for f does not exist.

Answer 3

- limits can be difficult to explain - they are hardest part of calculus ( for me anyway!)

Answer 4

Yeah, limits are difficult, and they're also the most fundamental concept in calculus really. It is important that you are very, very comfortable with epsilon-delta proofs of limits.

Answer 5

yes - i'm not very comfortable with them at all - i've tried reading up Spivak's chapter on limits in his Calculus bu it just won't stick i'm afraid. maybe i'll try again...

Answer 6

Spivak's treatment of limits is not easy to get through without help. It's just not an easy subject. Definitely read the chapter several times, and do what you can on the exercises. Don't lose hope if you struggle with the problems... Spivak's problems are all really hard.

Answer 7

And he's right when he says it's hopeless to continue without knowing the definition by heart. Memorize it however you have to memorize it :P

Answer 8

your last sentence - thats dead right . I'll have another try

Answer 9

The nice thing about really hard problems is that when you do solve them it feels amazing :) Also, it's good preparation for if you take serious math courses later on.

Answer 10

yes

Answer 11

i'll let you know how i get on - ty