# Squeeze Theorem

Squeeze Theorem

Let , , and be functions satisfying for all near , except possibly at . By the squeeze theorem, if f(x)=h(x)=L then g(x)=L. Hence, xsin equals zero if , or , since is squeezed between and . The theorem does not apply if , since is trapped but not squeezed. For the limit does not exist, because no matter how close gets to zero, there are values of near zero for which and some for which .

f

g

h

f(x)≤g(x)≤h(x)

x

a

a

lim

xa

lim

xa

lim

xa

lim

x0

n

1

x

n=1,2

3

xsin

n

1

x

-|x|

n

|x|

n

n=0

sin

1

x

n=0

x

x

sin=1

1

x

sin=-1

1

x