1
Math1013 Calculus I
Brief Answers to Class Problem Set
Class Problem Set: Using Derivatives: LHopitals Rule, Max-Min Problems, Antiderivatives
1. Find the limit:
e x e x 2 x
(a) lim
x0
x sin x
(d)
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Math1013-L2/L6 Calculus I
Brief Answers to Week 1 Class Problem Set
1. A taxi company charges two dollars for the rst kilometer (or part of a kilometer) and 20 cents for
each succeeding tenth of a kil
Math1013-L2/L6 Calculus I
Week 1: Brief Review of Functions
Before proceeding into calculus, you should get familiar with all basic notations and concepts about functions.
A function f is just a rule
1
Math1013-L2/L6 Calculus I
Basic Problems on Inverse Functions
Things to review:
What is a one-to-one function?
What is the relationship between f and its inverse f 1 (if exists), and their graphs?
1
Math1013-L2/L6 Calculus I
Basic Problems on Derivatives
Get use to the limit denition of derivative: (i.e., by looking at slopes of nearby secant lines)
f (x) = lim
h0
f (x + x) f (x) or
f (t) f (x
1
Math1013 L2/L6 Calculus I
More Basic Problems on Areas, Denite Integrals, Fundamental Theorem of
Calculus, and the Substitution Rule
Approximate areas using rectangles.
b
Understand the meaning of
1
Math1013-L2/L6 Calculus I
Basic Problems on Derivatives
Get use to the limit denition of derivative: (i.e., by looking at slopes of nearby secant lines)
f (x) = lim
h0
f (x + h) f (x) or
f (x + x)
1
Math1013 L2/L6 Calculus I
More Basic Problems on Areas, Denite Integrals, Fundamental Theorem of
Calculus, and the Substitution Rule
Approximate areas using rectangles.
b
Understand the meaning of
1
Math1013-L2/L6 Calculus I
Some Basic Problems on Applications of Derivatives: Extreme Values, Mean
Value Theorem and the Shape of a Graph
1. Find the absolute maximum and absolute minimum values of
1
Math1013-L2/L6 Calculus I
Some Basic Problems on Applications of Derivatives: Extreme Values, Mean
Value Theorem and the Shape of a Graph
Finding maximum and minimum of a continuous function on a c