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Student Signature:
Date:
Instructions: Answer all questions. Show all your work.
1. (10 marks) Let f(x) = 2/x.
(a) Define the “Newton quotient” for this function at a point a.
(b) Simplify this by cancelling “h” from the numerator and the denominator,
where possible.
(c) Find the limit of the “Newton quotient” as “h” approaches zero.
2. (10 marks) Let f(x) = 2x
2 − 4.
(a) Define the “Newton quotient” for this function at a point a.
(b) Simplify this by cancelling “h” from the numerator and the denominator,
where possible.
(c) Find the limit of the “Newton quotient” as “h” approaches zero.
3. (10 marks) Compute
lim
h→0
√
h + 4 − 2
h
5. (10 marks)
(a) For a function f(x) with a derivative f
0
(x) what is the equation
for its tangent line at a point x = a?
Let y = f(x) = x
3
.
(b) What is f
0
(x)?
(c) Find the tangent line to f(x) at a point a,
(d) Evaluate the tangent line at the point a = −1.
(e) Illustrate your answer on a graph.
6. (8 marks) Define the sets: A = {3, 4, 5, 6}, B = {5, 6, 4, 5}, C =
{2, 3, 8} and D = {2}. For these sets, find the following and illustrate
using Venn diagrams.
(a) A ∩ B
(b) (A\C) ∪ (C\A)
(c) B ∩ C ∩ D
(d) C ∪ D
