1. Compute cos
2. Compute sin
π
3
π
6
3. True or False (and give reasoning): Right-endpoint method will
always overestimate the area under a curve.
4. True or False (and give reasoning): If
inflection point of f .
d2 f
dx2
= 0 at x = c, then c is an
5. True or False (and give reasoning): If f (x) is continuous on [a, b],
(a)
= f 0 (c).
then there is at least one point c in (a, b) at which f (b)−f
b−a
√
2
1−x
6. Sketch a graph of y = 2x+1
. Include the coordinates of any local and
absolute extreme points and inflection points.
7. Find the volume of the largest right circular cone that can be
inscribed in a sphere of radius 3.
8. Graph a function
x
y
x<0
x=0
3
0<x<2
x=2
0
2<x<4
x=4
−2
9. Evaluate:
10. Evaluate:
11. Evaluate:
12. Evaluate:
Z
Z
Z
Z
that satisfies the following criteria:
Derivatives
0
y < 0, y 00 > 0
y 0 = 0, y 00 = 0
y 0 < 0, y 00 < 0
y 0 < 0, y 00 = 0
y 0 < 0, y 00 > 0
y 0 = 0, y 00 = 0
2θ2 sec2 (2θ) − 13θ6 + θ2 sin(2θ)
dx
θ2
cos(q)(tan(q) + sec(q)) dq
1
1
− 5/4
7 y
!
dy
csc(r) cot(r)
dr
2
13. Find the general anti-derivative
for:
√
5
7
4
f (x) = 13x − (12 − 2x) + 18 x2 − 1
14. Is this right or wrong? Give a brief reason why.
Z
x cos(x2 − sin(x2 )
sin(x2 )
+C
dx
=
x2
x
Z 0 √
15. Evaluate:
− 25 − x2 dx
−5
16. Evaluate:
Z 3
|x − 1| dx
0
17. Solve r(t) given
d2 r
dt2
=
2 dr
, |
t3 dt t=1
= 1, r(1) = 1