ZeePedia

Limits and Computational Approach

<< Limits (Intuitive Introduction)
Limits: A Rigorous Approach >>
img
Calculus and Analytical Geometry
MTH101
LECTUER ­ 10
Limits and Computational Approach
Some basic limit for
Table 2.5.1
(a)
(b)
Now for
(c)
Mth101
Page 27
img
Calculus and Analytical Geometry
Limits and Computational Approach
Theorem
If f1,f2 ,...........,fn are same functions
Thus we can write
Another useful result
Where k is constant
A polynomial is an expression of the form
Where bn , bn ­1,,.... , b1 , b0 are all constants.
Remark
Although the results ( a ) and ( c ) are
Example
stated for two functions f and g, these
Results hold as well for and finite number
of functions; that is, if the limits lim f1 (x),
Lim f2 ( x ),..........lim fn ( x ) all exists,
then
and
Mth101
Page 28
img
Calculus and Analytical Geometry
Limits and Computational Approach
Proof:
Limit involving
1
x
The following limits are suggested by
the graph of 1/x.
Table of numerical values
For every real number a the graph of
the function
Lim x2 = +00
Lim x = +00
x+00 x+00
Lim x2 = +00
Lim x = +00
x+00 x+00
Mth101
Page 29
img
Calculus and Analytical Geometry
Limits and Computational Approach
A polynomial behaves like its term of highest
degree as x+00
or x-00 more
precisely, if cn = 0
, then
Lim x3 = +00
x+00
Lim x3 = -00
Thus
x+00
Example
Example
For integer value of n
The graph has not value at x = 2
Example
Quick method for finding limit of rational functions
Mth101
Page 30