CHAPTER 2 : LIMITS
2.1 Modulus
 a  b  means the "nonnegative difference between a and b and is read as mod of a minus b".
\  a  b  = a  b if a > b
= 0 if a = b
= b  a if a < b
e.g.  7  5  = 2,  3  8  = 5,  8  = 8,  9  =  0
 9  = 9
Examples
If  x  = 8 then x = +8 or x = 8
If  x  9  = 3 then x 9 = +3 or x 9 = 3
i.e. x = 12 or x = 6
If  x  a  = d then x  a = d or x  a = +d
i.e. x = a  d or x = a + d
If  5x  2  =  x  then 5x2 = x or 5x  2 = x
i.e. 5x  x = 2 or 5x + x = 2
i.e. 4x = 2 or 6x = 2
i.e. x = 1/2 or x = 1/3
If 2  x  =  x  3  then 2 x = ( x3 ) Or 2x = ( x 3 )
i.e. 2x  x = 3 or 2x + x = 3
i.e. x = 3 or 3x = 3
i.e. x = 3 or x = 1

Index
2.1 Modulus
2.2 Inequalities
2.3 Limits Of Functions
2.4 Left Hand And Right
Hand Limits
2.5 Theorems On The
Algebra Of Limits
2.6 Evaluating Limits
2.7 Limits Of Trigonometric
Functions
2.8 The Exponential
Limits
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Chapter
3
