Math 172
Prerequisite Worksheet
Due: 29 Aug 2014
Show Appropriate Work, Justify Answers
1. (2 pts) Solve.
Name:
6
+1=x
x
2. (6 pts) Sketch a graph for each. Clearly label the scale on the axes and provide appropriate points.
(a) y = sin x
(b) y = cos x
(c) y = arctan x
3. (4 pts) Evaluate exactly - no calculators.
(a) sin (2π/3)
(b) cos (−π/3)
(c) tan (5π/4)
(d) arctan (1)
4. (4 pts) Use an appropriate triangle to simplify. [Hint: sin 2θ = 2 sin θ cos θ]
sin (2 arctan x)
5. (6 pts) Differentiate.
(a) f (x) = x2/3 ln x
(b) g(y) = arctan (2y + 6)
(c) h(t) =
Z t
1
2
ex + ln x dx
6. (12 pts) Evaluate.
ln x
(a) lim √
x→∞
x
Z √
(b)
Z
x−4
dx
x
π/6
(c)
sin (2x) dx
0
7. (2 pts) Evaluate the integral by interpreting it as an area. Provide justification.
[Hint: consider x2 + y 2 = 1]
Z 1p
1 − x2 dx
(a)
−1
8. (4 pts) Answer the following questions using the main course webpage:
(a) List the dates of the three common hour exams and the final:
(b) What percentage of your overall grade is the online homework (Webwork) worth?
(c) Videos on several topics can be found on the main course webpage. In the very first video,
what is the integral that’s presented in the second example?
(d) List three days/times (for example: Monday 11am) when a current M172 instructor is in the
Math Learning Center.