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Mathematics 137
February 18, 2015
Assignment 5 (due Wednesday, February 25 at the beginning of your tutorial)
Problem 1. Calculate
(a)
x sec2 (x2 )dx
(b)
1
cos2
0
(c)
1
1
( )
x dx
2
7x5 3 x dx
Problem 2. Calculate the area of the region in the rst quadran
Mathematics 137
October 8, 2014
Assignment 2 (due Wednesday, October 15 at the beginning of your tutorial)
Problem 1. Give , proof for the following statements
(a) limxc x = c for any c > 0,
(b) limx2 x 2 = 0.
Problem 2. Evaluate the limits that exist.
Mathematics 137
January 14, 2015
Assignment 4 (due Wednesday, January 21 at the beginning of your tutorial)
Problem 1. Give an example of a continuous function (not piecewise) with two
dierent horizontal asymptotes. Justify your answer. (Note that your ex
Mathematics 137
September 17, 2014
Assignment 1 (due Wednesday, September 24 at the beginning of your tutorial)
Problem 1. Let p be prime. Show that
p is irrational.
Problem 2. Given that 0 a b. Show that
a+b
b
a ab
2
Problem 3. For any natural n dene s(
Mathematics 137
October 29, 2014
Assignment 3 (due Wednesday, November 5 at the beginning of your tutorial)
Problem 1. Find f (c) if it exists.
cfw_
3x2 ,
x1
f (x) =
,
2x3 + 1, x > 1
and c = 1
Problem 2. Give an example of a function f such that f (x) exi