ath M 242 Section 010: Test #1
NAME: _
L/C
Please circle your l ab/discussion:
020
021
022
This test has 6 questions on 6 pages.
The p oints per page are 5, 5, 5, 5, C, 6.
Show your "work. A correct answer w ith l ittle or no reasoning may reeeive
a low score. (However, there is no need to be wordy.)
The 7th page has some formulas you can refer to if needed.
r
n^
i -,
i
i
[5 p oints] Question 1. Evaluate l im
1~
COy X
O
.
s\ ^
~2l
III/
/
_
rmO
^
[5 points] Question 2. Let R be the region b ounded by y = 1/x, y = 1/x'2,
and x 2. Find the area of t he region 7?,.
?
J_
'X
=>
-X =
at <x=o.)
ate.
1
-X
J-
x--t
-x
\J
2. +
is TOP
is
BOTTOM
[5 Question points] 3. Let R be the region bounded by the curves y -
x2 5x + 6 and y 0. Find the volume obtained when R is rotated around
the y-axis.
0
-tDP
c*- S'x -
J ...
r"
+ 5-x
2r\x
BOTTOM
f'2TT
[5 p oints] Question 4. Evaluate /
c~xcosx dx.
Jo
Of
-X
u = e.
O
d\i - cos
V = Si /\T
:r = /e-*jMx]
27T
f^,
L
-X
pas-h aa^. fake
Si*
#$
udu -
v = cos x
r
0
X-
X
Cos,
1
2rr
"coso
ZTf
-2TT
[e
^
CosZrr)
-e.
2.
_
\e
o
2ir
[6 points] Question 5. E valuate / ln(3x') dx.
lT)\A
?&TJ5.
I
*'/
-
= 2.
3-2,
Us e.
-
~
-
2,
U - Jh\
- 2_
[6 points] Question 6. Evaluate / see'5 a; dx.
U' . s>t a x
X
-/x
J-f-
sec -x -
x
-f
x
C