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#1 2007-09-16 19:27:40

Jay McGuire
Guest

Need Help Proving Limits

Using the definition of limit, prove:
1)that if limx->a g(x) = M ? 0, then lim x->a 1/(g(x)) = 1/M
2) limx->2 x^3 = 8

#2 2007-09-16 19:28:37

Jay McGuire
Guest

Re: Need Help Proving Limits

The ? is supposed to be a "does not equal" sign.

#3 2007-09-16 23:00:19

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: Need Help Proving Limits

Let’s assume first that M > 0.

If M < 0, we use the fact

, which can be proved separately. (Indeed the proof is nothing at all, since
.)) Then, by the above,
, and so
.

Last edited by JaneFairfax (2007-09-16 23:06:10)

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