There is another type of limit that we need to examine. For example, consider the behavior of the function f (x) = 1/x as x gets “larger and larger”. We see that as x increases without bound through positive values, the values of f (x) approach 0. This statement is expressed symbolically as lim 1/x = 0.
                                                                                                                                 x→∞
Similarly, as x decreases without bound, the values of f (x) also approach 0 and we write lim lim 1/x = 0.
                                                                                                                              x→ - ∞  

In general, the statement

lim f (x) = l.
x→∞

means that as x increases without bound, the values of f (x) approach the number l. Similarly, the statement lim f (x) = l  means that as x decreases without bound, the values of f (x) approach l.
            x→ - ∞
The following examples deal with the calculation of some limits at infinity.
 
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