ASSIGNMENT 3 for SECTION 001
This assignment is to be handed in. There are two parts: Part A and Part B.
Part A will be graded for completeness. You will receive full marks only if every question has been completed.
Part B will be graded for correctness. You will receive full marks on a question only if your answer is correct
and your reasoning is clear. In both parts, you must show your work.
Please submit Part A and Part B separately, with your name on each part.
Part A
From The Mathematics Survival Kit:
Complete question 1 on the following pages: 166, 168
Complete question 2 on page 170
From Calculus: Early Transcendentals:
From section 2.2, complete questions: 2, 4, 6, 8, 10, 12, 14, 16, 26, 32, 34(a)
From section 2.3, complete questions: 2, 4, 6, 8, 10, 14, 16, 20, 22, 24, 26, 28, 30, 36, 40, 46
Part B
p
1
sin
x3 + x2 , if it exists.
x→0
x
1. Find lim
2. Let lim f (x) = 7, lim f (x) = 3 and y = f (x) be a line. What is the slope of the line?
x→−1
3. Let f (x) =
x→1
1
.
(x − 1)3
4. (a) Find lim f (x), if it exists
x→1−
4. (b) Find lim f (x), if it exists
x→1+
4. (c) Sketch the graph of y = f (x)
4. Find an example of functions f and g such that lim f ◦ g(x) exists, but lim f (x) and lim g(x) do not.
x→0
5. Let
f (x) =
Prove that lim f (x) does not exist.
x→0
0
1
if x is rational
.
otherwise
x→0
x→0