Quote:
Originally Posted by BlakeM
As for a tutor, you could possibly message Mowicz. I believe he did a review session for us last year on either 1Z04 or 1ZZ5, cant' remember. Couldn't hurt to ask.
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I just tutored 6 people for tomorrow's test, and I'm booked to help another 2 tomorrow. 0:
I'm a bit surprised at how much demand there is for tutoring, haha. (It makes me realize what an overpaid profession academia is though...I made $150, just today) I'm also a bit confused as to why so many people are asking for me specifically, when there are so many qualified math tutors! (Word of mouth perhaps)
Here are some general tips, from my own experience as well as from what areas were consistently covered in my tutoring sessions today:
a) Know what a sequence is (ie. an infinite 'string' of numbers)
b) Know what a series is (ie. the sum of the terms of a sequence)
c) Know the "convergence test." That is:
If {a_n} is a sequence, and you're looking at the sum from (n = 1 to infinity) of a_n...the terms had better get arbitrarily small, or your sum will blow up.
In other words, if lim[n->infinity] a_n =/= 0, then the series
must diverge.
**Note: The converse does not hold in general! But if say, you have an
alternating sequence then it converges if and only if the limit of the a_n's is 0.
IMPORTANT: Always always ALWAYS do this check first. It can save you a lot of hassle, if you can conclude right off the bat that a series diverges.
d) Know the "comparison test." That is:
If {a_n} and {b_n} are two sequences, and a_n < b_n for all n...then if you're looking at the sum from (n = 1 to infinity) of b_n and it's finite (ie. convergent), the sum from (n = 1 to infinity) of a_n must be finite as well.
e) Know the "integral test." I can't explain this one as well with text (too bad I can't draw a picture), but the idea is that you think of the terms of your sequence as a 'riemann sum' of an integral, where you've partitioned the x-axis into pieces each having length 1.
f) Look through your lecture notes for any 'tricks' your professor did in class. You can expect these will probably be on the test!
g) Any 'really hard questions' on your practice exams are from several years ago...they were 'tricks' presented in class, that they were expected to know.
(In particular, there's one question which is the sum of (sin(x)/3)^n. You're expected to multiply the sum by sin(x), then divide by the original sum, and compare what you get with the original sum (which is pretty evil!))
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Hope that helps!
