Study Guide
Test 1
Summer 2011
Carter
1. Be able to complete the square of a quadratic function and sketch the graph of the
resulting parabola. [There will be one question of this type that is worth 10 points].
See
http://www.youtube.com/watch?v=_GBtlR4m67g
and
http://www.youtube.com/watch?v=YW1MVXyhJZE
2. Definitions and proofs:
(a) Be able to state the definition of a limit (p. 109). See also
http://www.youtube.com/watch?v=wSTJLUAu5ZI
(b) Be able to state the definition of a continuous function. See page 83.
(c) Be able to prove that limh→0+
sin (h)
h
= 1. See page 100-101 or
http://www.youtube.com/watch?v=o6S6RbfhRTU
(d) Be able to prove that limh→0+
cos (h)−1
h
= 0. See text or
http://www.youtube.com/watch?v=encQhh2JeYc
(e) Use the previous two items to compute
lim
sin (x + h) − sin (x)
h
lim
cos (x + h) − cos (x)
h
h→0
or
h→0
See p. 167-168.
[There will be 3-4 items chosen from item 2 for between 15 and 20 points].
3. Be able to compute limits as on p.97-98 #1 –26, p. 103 # 19-40, and p. 125 # 23-40.
4. Be able to use the rules of differentiation to compute derivatives, slopes at points, and
equations of tangent lines as in p. 139 # 23–34, p. 148 # 17 – 34, p. 170 # 1 –30, p.
178 # 9–70, p. 208 # 28–53. [up to 9 problems. 45 points]. See also
http://www.youtube.com/watch?v=IApiSXg4yXE
5. Be able to solve the vertical motion problems such as p. 158 # 12, 30–33. [One
question, 10 points].
1