1. Evaluate:
R 2θ2 sec2 (2θ)−13θ6 +θ2 sin(2θ)
θ2
dx
√
5
2. Find the anti-derivative for: f (x) = 13x7 − (12 − 2x)4 + 18 x2 − 1
3. Evaluate:
R0
√
−5 −
25 − x2 dx
4. True or False (and give reasoning): Right-endpoint method will always
overestimate the area under a curve.
5. True or False (and give reasoning): Midpoint method is always a better
approximation than left or right-endpoint methods for estimating the area
under the curve.
√
2
1−x
. Include the coordinates of any local and
6. Sketch a graph of y = 2x+1
absolute extreme points and inflection points.
1
7. Find the volume of the largest right circular cone that can be inscribed
in a sphere of radius 3.
8. Graph a function that satisfies the following criteria:
x
y
Derivatives
x<0
y 0 < 0, y 00 > 0
x=0
3 y 0 = 0, y 00 = 0
0<x<2
y 0 < 0, y 00 < 0
x=2
0 y 0 < 0, y 00 = 0
2<x<4
y 0 < 0, y 00 > 0
x=4
−2 y 0 = 0, y 00 = 0
9. Compute cos(π/3)
10. Compute sin(π/6)
2