Mat.h 1100-3
Babenko V.
December 3. 2015
Test 4
Name:
UID#:
This is a closed book Test. No books, laptops, or messaging are permitted.
NO calculators are allowed. You have 15 problems, they are equal in weight.
The entire exam is worth 15 points. For full credits show all work! Box your
answer so it is easy to locate. You have 60 minutes.
GOOD LUCK!!!
1
-
1. Approximate the area under the curve over the specified interval by
using the indicated number of subintervals (or rectangles) and evaluating the
function at the right-hand endpoints of the subintervals.
2 from x = 0 to x = 2; 2 subintervals.
f (x) = 5x x
—
5.1- i
10
4
2. Evaluate the definite integral. (i0
4x)dx
S id j
—k—
4Q
—a
t)
o-SO--O.
3. Evaluate the definite integral.
f(4x
—
2
6x
_s)\
=
=
—
(_
2
z.-
-
2
—
5x)dz
4. Find the area between the curve y
x=—4tox=—l.
—
=
((
2 + lOx +24 and the x-axis from
x
2.
5
4
3
5. In this problem, equations are given whose graphs enclose a region. Find
; x = 0; x = 1.
2
2 + 7; g(x) = —x
the area of the region. f(x) = x
S
3
6. Equations are given whose graphs enclose a region. Find the area of
the region. f(x) = x
2 + 3x. (Plug in numbers, but DO NOT
; g(x) = 2x
3
simplify)
2-
2x-2
2i-\FT2
2
.._—
C223O
0
‘-I
4
—
—
-
4
7. Find the average value of the function over the given interval.
f(x)
=
81
—
over [0, 9j.
-
A
—
b—
9
—
9_
)\o-
-
3
8. Evaluate the improper integral.
—1
I -1’
-DO
—‘
—‘
\_
-
0’-—>
_Q5
\•‘
5
9. Evaluate the improper integral.
00
I
-00
8x
dx.
2
)
1
2+
(x
0
-
-
V R
0
_\
/ +
.y
—
—‘
—
\\
z
6
10. In this problem, p is in dollars and x is the number of units.
Find the producer’s surplus for a product with demand function p
33/(x + 1) and supply function p = 1 + 0.2x.
---
c.?— x
0
o
2
.Z
32I
Q2) -‘-L2
—0
2-
jO
3
-‘7
2
-
\1O
-
-c
20
i+O.i •(
2
(0
-
‘Iv.
7
=
11. Give the domain of the function.
6x x
3
4x—y
—
S
X:j/
L
12. Evaluate the function at the given values of the independent variables.
x + xy
2
x—y
13. If z
-
=
—
2 + 8x + 3y
3x
3
—
x=6,y=7
7y + 2, find
‘2
8
and
14. If z
=
y
2
x
—
, find
2
7xy
z
and z.
2
I4
1’
15. If z
=
y
2
x
—
, find z and z,.
2
7xy
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
Total
9
/10
/10
/10
/10
/10
/10
/10
/10
/10
/10
/10
/10
/10
/10
/10
/150
/15