For a hint on #22 take a look at Example 6 on p. 103. Basically, for ratios involving square roots you need to multiply the numerator and denominator by the conjugate.
As for the squeeze theorem.... I had a Russian professor once who called it the "Drunk and Policeman Theorem". Basically, imagine a drunk guy stumbling around between two burly policemen (or woman, hey, it is your imagination). The drunk can stumble around but he is going to the station because that is where the policeman are going.
With that said, sometimes you get a limit which you can't figure out using the algebraic "laws" of this section (cf #37 or Example 11). However, if you can bracket the limit you are wondering about between two limits you can figure out, you know where the one in the middle is going. That is, if you can find two functions whose limits you do know (call them f(x) and h(x)) such that
lim f(x) <= Crazy Unknown Limit <= lim g(x)
then you know where the "crazy unknown limit" is going. Take a good look at example 11, p 106.
email: berwald AT math DOT montana DOT edu (anti-spam: replace green with normal symbol) phone: 406.994.5360 office: Wilson 2-232 office hours: MTR 11-12; LC Fri 11-12; and by appt.
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3 comments:
On #22 how do you evaluate the limit? Also how does the Squeeze Theorem work. I am cunfused on it.
Ask in class tomorrow if you still have questions. (Sorry, out of town this weekend.)
For a hint on #22 take a look at Example 6 on p. 103. Basically, for ratios involving square roots you need to multiply the numerator and denominator by the conjugate.
As for the squeeze theorem.... I had a Russian professor once who called it the "Drunk and Policeman Theorem". Basically, imagine a drunk guy stumbling around between two burly policemen (or woman, hey, it is your imagination). The drunk can stumble around but he is going to the station because that is where the policeman are going.
With that said, sometimes you get a limit which you can't figure out using the algebraic "laws" of this section (cf #37 or Example 11). However, if you can bracket the limit you are wondering about between two limits you can figure out, you know where the one in the middle is going. That is, if you can find two functions whose limits you do know (call them f(x) and h(x)) such that
lim f(x) <= Crazy Unknown Limit <= lim g(x)
then you know where the "crazy unknown limit" is going. Take a good look at example 11, p 106.
I hope this helps.
BEN
(instructor, M181-6)_
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