Math 126 Test 3 March 13, 2003
Perform the indicated operation 1 point each
1.
∫ e3x dx
2.
Dx ( e3x)
3.
∫ sin 4x dx
4.
Dx( sin 4x)
5.
∫ cos 3x dx
6.
Dx ( cos 3x)
7.
( x2 + 25 )1/2
8.
(x + 5)2
9.
∫ dx / (3x + 1)
10.
∫ dx / (3x + 1)4
11.
∫ dx =
12.
∫ 3 dx =
13.
∫ x3 dx =
14.
=
15.
=
16.
17.
18.
=
19.
=
20.
=
21.
∫ sin (3x) dx =
22.
∫ 5 sin (3x) dx =
23.
∫ cos(x / 2) dx =
24.
∫ 5 cos (3x / 2) dx =
25.
∫ ex dx =
26.
∫ e - x dx =
27.
∫ e x/2 dx =
28.
∫ 3 e4x dx
=
29.
=
30.
3 points each
Evaluate the limit
31.
limit
((1-cos x) / x2)
x v0
32. Limit (ex / x)
x 0
33. limit (sec x - tan x )
x v π/2 -
34.
limit xx
x v 0+
35. limit x1/x
x v ∞
36. limit (1+x)1/x
x v 0
37. Limit (cot x/cot 2x)
x v 0+
Evaluate the integral
38.
Write an expression for the nth
term of :
39. 1,3,5,7,9,…
40.
1, 4,7,10,…
State whether the sequence converges or
diverges.
41.
an = 1 + (-1)n
42.
43.
an = (3n / 4n )
44.
an = (n - 2)! / n!
Find the sum:
45.
1 + 4 + 7 + 10 + 11 + .........151
46.
47.
Tell whether the series converges or
diverges - 2
Tell why - 1
48.
49.
50. 
51.
52.
53.
54.
55.
1 + 1/ √2 + 1 /
√3 + 1/ √4 ...
56.
1 + 1/4 + 1 / 3 + 1/16 + .....
57.
Use the integral test to determine whether or not the series converges
or diverges and why.
