On-line Math 21

On-line Math 21

1.4  Computing limits

Example 1

lim
x® 0 
x sin æ
ç
è
1
x
ö
÷
ø
= 0.

Solution

In this case, noting that, no matter what x is,
-1 £ sin æ
ç
è
1
x
ö
÷
ø
£ 1,
then
-|x| £ x sin æ
ç
è
1
x
ö
÷
ø
£ |x|.
So, taking -|x| = f(x) , xsin(1/x) = g(x) , and +|x| = h(x) , and noting that

lim
x® 0 
-|x| = 0 =
lim
x® 0 
+|x|,
the squeeze theorem implies that

lim
x® 0 
x sin æ
ç
è
1
x
ö
÷
ø
= 0.

Copyright (c) 2000 by David L. Johnson.


File translated from TEX by TTH, version 2.61.
On 12 Oct 2000, 23:55.