On-line Math 21

1.4  Computing limits

Example 3 Compute

lim x® -1  Ö   x3+2x+7   .

Solution

To be fair, we really don't have the theory to claim this (yet), but we can argue simply that, since

lim x® -1  x3+2x+7 = lim x® -1  æ è Ö   x3+2x+7   ö ø 2   = lim x® -1  Ö   x3+2x+7   lim x® -1  Ö   x3+2x+7   ,

and

lim x® -1  x3+2x+7 = (-1)3+2(-1)+7 = 4,

then

lim x® -1  Ö   x3+2x+7   = 2.

Copyright (c) 2000 by David L. Johnson.