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Material Type: Lab; Professor: Santos; Class: Calculus II; Subject: Mathematics; University: Community College of Philadelphia; Term: Unknown 1989;
Typology: Lab Reports
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Math 172 Prerequisites 1
Instructions: This is a list of some material that is essential prerequisite for this course. That is, your instructor expects that you have a definite idea of the notions expounded below and that you be able to solve the problems below without any review. If you find yourself having trouble on some items below you should seek immediate help from your instructor or from the tutors in the Learning Laboratory.
Essential prerequisites include:
(a) Graphing quadratic curves. (b) Knowing elementary exponential, logarith- mic, and trigonometric identities. (c) Manipulation of algebraic fractions.
(d) Completion of the square. (e) Knowing the basic differentiation rules. (f) Knowing the basics of integration. (g) Knowing integration by substitution.
You should be able to quickly answer all questions below without needing any review.
(x − 2)^2 9
(y + 1)^2 4
− 1
|x − 1 | dx.
∫ (^) π
−π/ 2
cos x dx.
(a) y =
x + 1 x − 1 (b) y = sec(2x)
(c) y =
4 − x^2 (d) y = x^3 e^3 x
x
x^2
x − 2
1 + x−^2 /^3 = x−^1 /^3
1 + x^2 /^3.
(a) arccos
(b) arcsin
π 2
< x < π and sin x =
, find tan x.
π 2
and tan θ =
x
, find cos θ.
(a) limx→ 2 −
(x − 1)(x − 2) x + 2
(b) limx→0+ 1 − cos(2x)
(c) limx→ 0 sin 2x tan 3x
(d) limx→− 1
x^2 − 1 x + 1
(a) f (1) (b) f (3) (c) limx→ 1 f (x) (d) limx→−1+ f (x)
(e) limx→−∞ f (x)
(f) limx→ 3 − f (x)
(g) limx→3+ f (x)
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
0
1
2
3
4
5
6
7
Figure 1: Problem 13.
(sin x)ecos^ x^ dx.
cos x 1 − sin x
cos x 1 + sin x
and use
it to find
sec x dx.
1 − x 1 + x
dx.
By: Dan JACOBSON and David A. SANTOS Last Revision: January 12, 2008