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1 An Introduction to Complex Numbers
1.1 Introduction
We are familiar with quadratic functions of the form
f(a:) = a332 + ta: + c,
where a, b, and C are Legalw DAMS— . Such functions, as we
saw in
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1
Now we know from hypothesis (ii).that 6A and so,
rearranging we have that
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Now to (ﬁnally!) prove L’Hopital’s rule!
Proof of L’Hé
5.3 Integration by Trigonometric Substitution
Previously, we learned how to integrate by using the method of
substitution. This method allowed us to change a d M -
l 00 an integral into one that we ca
5.2 Integrating Products of Trig Functions
Consider the following integral:
/00s(:r)si112(23) dx = S (1050:)
a 1 )
M—bw :-co.s(x
This is easy; we can just use chLQFLrLﬂ rgif; iﬂ
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1
An Introduction to Complex Numbers
1.1
Introduction
We are familiar with quadratic functions of the form
f (x) = ax2 + bx + c,
where a, b, and c are r
n
. Such functions, as we
saw in high school ma
Practice Term Test 1
Math*1210, Winter 2015
Friday, February 6 at 5:30 pm
Last Name:
First Name:
Instructions for right now:
Ensure that all elds are clearly lled out on the rst and second pages of t
We come up with six new formulas:
w
I?»
. QEQFCSHIBED : 7:—
d _l
0 ——-(arcoos(:r) :
dx "——-—-l _ x1
d
——"l
o dJars an(_a:) I + x1
dr < > ——'—'——-—r._
. -— z
d3: arocse w) b4 x14
o E;(arcseo(
We know that for f to be a function, the curve representing must
pass a V er—h‘ cal
line 1; es+
For the inverse function to exist, f must not only pass a vertical
line test, but also a hm line test. I
Part A: Quick Answer — 15 marks
Read each question carefully and please ensure that you ﬁll in your ﬁnal answers in the boxes
provided at the right side of the page. Each correct answer is worth 1 mar