Infinity ( ¥) occurs many times in calculus. It's not just some sort of science-fiction invention, it has meaning, in terms of limits. In the case of
it means that, as x gets larger without bound, f(x) settles down and gets closer to L .
means that, as x gets larger and larger, so does f(x) .
Finally, it might happen that a function might itself get large without bound, as x goes to a real number a . We then say that
None of this explanation really offers much insight on how you can compute limits of more than the simplist examples. There are a few standard theorems and techniques that make these computations straightforward.
Example 1 lim x® ¥ Ö x2+1 -1x
Example 2 lim x® ¥ 2x3+x2+x-6x3+4x+5
Example 3 lim x® 1- 1x-1
Example 4 lim x® ¥ x2+5x-6x3+x+5
Exercise 1 lim x® ¥ Ö x2+2x-1 -x =
Exercise 2 lim x® ¥ x2+5x-6x3+5 =
Exercise 3 lim x® 1+ x2-5x+6x-1 =
Exercise 4 lim x® ¥ x3-3x+6x2-x+5 =
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Copyright (c) 2000 by David L. Johnson.