1322Assign1SolutionS14 - MAT1322-3X Solution to Assignment...

MAT1322-3X Solution to Assignment 1 Summer 2014
Solution to Assignment 1
MAT1322-3X, Summer 2014, Total = 10 marks (Note that no all questions are marked)
1. Use the definition of improper integrals to determine if each of the following improper
integral is convergent or divergent. If it is convergent, find its value.
(a) (2 marks)
2
1
1
1
dx
x
-
+
∫
;
(b) (not marked)
2
ln
dx
x x
1 1
lim 2 lim 1 2 3
 
= = + =
 
1
∞
∫
;
2
(b)
ln
ln
1/2 1/2
ln2
2 ln 2
=
→∞ →∞ →∞
1
2. Use the comparison test to determine if each of the following improper integral is convergent
or divergent.
(a) (2 marks)
5 2 4 1
1 x
dx
x x
∞
+
∫
;
(b) (2 marks)
5 2 4 0
1 x
dx
x x +
∫
;
(c) (not marked)
2
/2
1