2012/2013 M. Ilyas Hadikusuma, M.Eng Matematika Terapan 1 TIF 21101 APPLIED MATH 1 (MATEMATIKA TERAPAN 1) Week 11 Limits
Aug 08, 2015
2012/2013 M. Ilyas Hadikusuma, M.Eng Matematika Terapan 1
TIF 21101APPLIED MATH 1
(MATEMATIKA TERAPAN 1)
Week 11Limits
2012/2013 M. Ilyas Hadikusuma, M.Eng Matematika Terapan 1
Limits
OverviewSometimes we meet the words “almost” or “approach” in our daily life. For examples : “Today, I almost late for the class” or “He almost got an accident when he tried to pass that fast motorbike”, etc.In math, the word almost or approach is known in term of Limits.Do you know what the term of limits for?
2012/2013 M. Ilyas Hadikusuma, M.Eng Matematika Terapan 1
Limits
Definition
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Lxfcx
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ifthat so 0 a exists there
0 eachfor that means statement The
number. real a beL let and c)at possibly (except
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2012/2013 M. Ilyas Hadikusuma, M.Eng Matematika Terapan 1
Limits
If f is a function, then we say:A is the limit of f (x) as x approaches c if the value of f (x) gets arbitrarily close to A as x approaches c. This is written in mathamatical notation as:
Notice the important fact that whether or not the notation above is true, does not depend upon the value of f (x) when x = c. In fact, f (x) need not even be defined when x = c. In other word, there’s no limit if the limit of function equals to 0.
c
2012/2013 M. Ilyas Hadikusuma, M.Eng Matematika Terapan 1
Limits
For example:
However, using factorization, we can simplify the function into :
2012/2013 M. Ilyas Hadikusuma, M.Eng Matematika Terapan 1
Limits
Limit of a function can be identified if the value of left limit and right limit is equal. Ex. :A function is given by :
Check if the function is exist
4x, if x ≤ 4
4x + 6, if x 4
2012/2013 M. Ilyas Hadikusuma, M.Eng Matematika Terapan 1
Limits
Try this,
Using table :
From the table, the right and left limit show the nearest value to 6, therefor there is a limit value for x3
2012/2013 M. Ilyas Hadikusuma, M.Eng Matematika Terapan 1
Limits
Infinite Function of Limit
It will result in : - or / Rules :
2012/2013 M. Ilyas Hadikusuma, M.Eng Matematika Terapan 1
Limits
For division of polynomial, there are some rules :