Squeeze Theorem Worksheet
A Grade 12 Calculus worksheet focusing on understanding and applying the Squeeze Theorem to find limits.
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Squeeze Theorem Worksheet
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Read each question carefully and provide detailed solutions, showing all steps. Use the Squeeze Theorem where appropriate to evaluate limits.
1. State the Squeeze Theorem. What are the three conditions that must be met for the theorem to apply?
2. Given that for all x near 0, -x² ≤ f(x) ≤ x², then by the Squeeze Theorem, lim (x→0) f(x) = .
3. If 4 - x² ≤ g(x) ≤ 4 + x² for x ≠ 0, then lim (x→0) g(x) = .
4. Use the Squeeze Theorem to evaluate lim (x→0) [x² cos(1/x)]. Show your work.
5. Consider the function f(x) such that for x ≠ 0, 1 - x² ≤ f(x) ≤ 1 + x². Evaluate lim (x→0) f(x).
6. Which of the following is a necessary condition for the Squeeze Theorem to be used?
The functions must be continuous.
The limit of the outer functions must be different.
The function being squeezed must be differentiable.
The limits of the two bounding functions must be equal.
7. The Squeeze Theorem can only be applied when the function is oscillating between two other functions.
True
False