Math 7 Test
Mr. Garcia
Name
Instructions.Show all your work.
1. Use
lim
n!1
the
n
aX
b
f (x) dx
=
a
n
b
Z
formula:
f
b
a+
a
n
i=1
Z
to evaluate:
3
(x2 + 2x
3)dx
2
2. Evauate:
Z
3. Evaluate:
i
Z
3
dx
2
=3
=4
(5x
2
3)
1 + sin x
dx
cos2 x
4. Evaluate:
Z
=6
1
Math 7 Test 2
Mr. Garcia
Name
Instructions.Show all your work. No partial credit will be given for stating answers. Box your answers.
1. Discuss the dierentiability of f (x) at x = 0; x = 1
8
2x if x < 0
<
x x2 if 0 x 1
f (x) =
:
x 1 if x 1
2. Use the den
More on Approximating area with rectangles.
consider the function: f (x) = 16 x2 ; suppose we want to approximate the
area under the curve with rectangles on the interval [0; 4] with a partition of
width 0:5
y
16
14
12
10
8
6
4
2
0
0.5
1.0
1.5
2.0
2.5
3.0