Chapter 2
Chapter 2Limits and ContinuityKT00403 ENGINEERING MATHEMATICS
1
Limit of a Function and Limit Laws
Definition We write
And say the limit of f(x), as x approaches c, equals L
If we can make the values of f(x) arbitrarily close to L (as
close to L as we like) by taking x to be sufficiently close to c
(on either side of a) but not equal to a.
Alternative notation: f(x) L as x cf(x) approaches L as x
approaches c
A limit that does not existNo single number that f(x) approaches
as x approaches 0
Example
Simplify as you can before substitute
Exercise1. Evaluate the following limits
Answer:39- 1/11Direct substitution doesnt always work!
Exercise
One Sided Limit
Exercise1. Find if it exist
2. Let
a. Does exist?
b. Find
AnswerNot exista. Not exist b. 2
Limits involving (sin /)
Example:
Continuity
Continuity
*any polynomial is continuous everywhere*any rational function
is continuous wherever it is defined
*continuous function: a functions whose graph has no hole or
break
Limits Involving Infinity: Asymptotes of GraphLimits at infinity
of rational functionsExample:
Solution:Divide the numerator and denominatorby the highest
power of x in the denominatorHorizontal asymptotes
Horizontal asymptotes:y=1 and y=-1
Oblique asymptotesIf the degree of numerator of a rational
function is 1 greater than theDegree of the denominator Divide the
numerator by the denominator Linear function + remainder
Vertical asymptotes
Tutorial 2
Exercise 2.2 : 2,4,11,22,28,34,47,54Exercise 2.4 :
1,4,12,25Exercise 2.5 : 2,6,25,40Exercise 2.6 : 19,28,67,102
