How does one determine limits for complex rational functions
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How does one determine limits for complex rational functions

[From: ] [author: ] [Date: 13-09-25] [Hit: ]
......
Suppose you were given a complex function: e.g:

(2x^3+10x^2+12x)/(x^3+2x^2)

Now if you were supposed to determine the limit as x approaches + infinity or
when x approaches V.A. 3

How would you do this without graphing aid? Its hard to imagine a rational graph with complex roots in your head.

-
given P(x) / Q(x) and x ---> ± ∞ it is easy to show the answers are

1) infinity if deg P > deg Q

2) ratio of coefficients of greatest powers if deg P = deg Q

3) 0 if deg P < deg Q

thus in this problem it is 2 / 1 { as typed ]
1
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