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Math 142 In-Class Quiz from Thursday 2/9/06 Due at beginning of class on Monday 2/13/06
The class performance on Problem 1 from Exam 1 was absolutely unacceptable: the average score was only 5.6 and the median was only 5 (out of 10 points). You were told
Math 142
Techniques of Integration Trigonometric Integrals
The book gives lots of rules/strategies. Read them but do NOT memorize. Use logic instead, as done below! Recall the following natural pairings (in terms of derivatives): sin cos tan sec cot csc
Partial Fractions If y = f (x) and y = g(x) are polynomials, then it follows from a theorem in algebra that f (x) g(x)
rational function
=
P (x)
a polynomial
+ F1 (x) + F2 (x) + . . . + Fk (x) ,
partial fraction decomposition
(1)
where each partial fracti
Indeterminate Forms - LHpitals Rule o At x = u, has the indeterminate form if lim f (x) =
xu
and lim g(x) =
xu
(1) (2) (3) (4) (5) (6) (7)
f (x) g(x) f (x) g(x)
0 0
0 0 0 1
0 0 0
f (x) g(x) f (x) g(x) [f (x)]g(x) [f (x)]g(x) [f (x)]g(x)
0 00 0 1
HERE: u