Determining Limits Using the Squeeze Theorem
AP Calculus AB · Flashcards
AP CALCULUS AB · FLASHCARDS
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QUESTION
Determine
lim
x
→
0
x
4
sin
(
1
x
)
\lim_{x \to 0} x^4 \sin(\frac{1}{x})
lim
x
→
0
x
4
sin
(
x
1
)
using the Squeeze Theorem.
QUESTION
Find
lim
x
→
0
x
2
sin
(
1
x
)
\lim_{x \to 0} x^2 \sin(\frac{1}{x})
lim
x
→
0
x
2
sin
(
x
1
)
using the Squeeze Theorem.
QUESTION
Find
lim
x
→
0
x
2
cos
(
1
x
)
\lim_{x \to 0} x^2 \cos(\frac{1}{x})
lim
x
→
0
x
2
cos
(
x
1
)
using the Squeeze Theorem.
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ANSWER
0
0
0
. Since
−
x
2
≤
x
2
cos
(
1
x
)
≤
x
2
-x^2 \leq x^2 \cos(\frac{1}{x}) \leq x^2
−
x
2
≤
x
2
cos
(
x
1
)
≤
x
2
and both bounds approach
0
0
0
.
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