Determining Limits Using the Squeeze Theorem
AP Calculus BC · Flashcards · Application
AP CALCULUS BC · FLASHCARDS
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QUESTION
Find the limit of
x
2
cos
(
1
x
2
)
x^2 \text{cos}(\frac{1}{x^2})
x
2
cos
(
x
2
1
)
as
x
→
0
x \to 0
x
→
0
using the Squeeze Theorem.
QUESTION
Find the limit:
x
2
cos
(
x
)
x^2 \text{cos}(x)
x
2
cos
(
x
)
as
x
→
0
x \to 0
x
→
0
using the Squeeze Theorem.
QUESTION
Evaluate the limit of
x
3
sin
(
1
x
)
x^3 \sin(\frac{1}{x})
x
3
sin
(
x
1
)
as
x
→
0
x \to 0
x
→
0
using the Squeeze Theorem.
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ANSWER
0. Bounded by
−
∣
x
3
∣
≤
x
3
sin
(
1
x
)
≤
∣
x
3
∣
-|x^3| \leq x^3 \sin(\frac{1}{x}) \leq |x^3|
−
∣
x
3
∣
≤
x
3
sin
(
x
1
)
≤
∣
x
3
∣
, both approach 0.
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