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, sin equals zero if , or , since sin 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
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lim
xa
lim
xa
lim
x0
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1
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n=1,2
3
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1
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-||
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n
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n=0
sin
1
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n=0
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sin=1
1
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sin=-1
1
x