Infinite Function

Infinite function indicates the limitless who are derived from Latin word infinities mean unbound ness. History says if we remove some value or adds some value to infinite, it will remain same like removing glass of water from ocean or adding bucket of water to ocean, which results same infinite. so infinite which is indicated by letter ∞.It makes an indication saying that whenever you need use of infinite then it can be used  as if it was a number  same as the number used in mathematics but it refers to a infinite quantity

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Definition of infinite function:

            A function f  becomes positively infinite or approaches infinity as x tends to a if for a positive number G, there exists a positive number  `delta`  such that  f(x) > G, whenever    0 < | x - a | < `delta` this fact is expressed in writing,
               Lt         f(x) = + `oo`          
             x `->` a
            A function f  becomes negatively infinite or approaches minus infinity as x  tends to a if for a given number G, there exists a positive number `delta` such that,
             | f(x) | < G wherever 0 < | x - a | < `delta` and is written as
                Lt          f(x)  =     - `oo`         
             X `->` a
           If function values keep decreasing without bound and as x approaches a given value, we say the limit is -Infinity.
            In general, f becomes infinity or approaches infinity as x tends to a for a given number G, there exists a positive number `delta` such that,
                     | f(x) | < G whenever
                      0 < | x - a | < `delta`
                     And is written as,
                  Lt      f(x) = `oo`         
              x`|->` a
If function values keep increasing without bound and as x approaches a given value, we say the limit is Infinity.
These definitions can also be modified when instead of x tending to + `oo` , - `oo`         


I am planning to write more post on Definition of Positive Correlation and Square Root Definition. Keep checking my blog.

Examples problem for infinite function:

Problem 1:
                f(x) = 1 / 2( x +1 )
          Answer: x = -1
Problem 2:
                f(x) = ( x² + 1 ) / ( x² +1 )
         Answer: x =1, -1
Problem 3:
         f(x) =  (x² + 2x – 8) / ( x² – 4)
         Answer: x = 2, -2