Squeeze Theorem Worksheet
A Grade 9 math worksheet covering the Squeeze Theorem with various question types.
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Squeeze Theorem Worksheet
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Read each question carefully and answer to the best of your ability. Show all your work for full credit.
The Squeeze Theorem (also known as the Sandwich Theorem) is a powerful tool in calculus used to determine the limit of a function by comparing it with two other functions whose limits are known.
If we have three functions, f(x), g(x), and h(x), such that f(x) ≤ g(x) ≤ h(x) for all x in an interval around 'a' (except possibly at 'a' itself), and if lim (x→a) f(x) = L and lim (x→a) h(x) = L, then lim (x→a) g(x) = L.
1. What is another name for the Squeeze Theorem?
The Limit Theorem
The Sandwich Theorem
The Comparison Theorem
The Bounding Theorem
2. For the Squeeze Theorem to apply for a function g(x), what must be true about the limits of the two bounding functions f(x) and h(x) at a point 'a'?
They must be different.
They must be equal.
They must be zero.
They must be undefined.
3. The Squeeze Theorem can only be applied when the function g(x) is continuous.
True
False
4. If f(x) ≤ g(x) ≤ h(x) and lim (x→a) f(x) = 5 and lim (x→a) h(x) = 7, then the Squeeze Theorem states that lim (x→a) g(x) must be between 5 and 7.
True
False
5. The Squeeze Theorem is used to find the of a function.
6. For the Squeeze Theorem, the function g(x) must be by two other functions.
7. If lim (x→a) f(x) = L and lim (x→a) h(x) = L, and f(x) ≤ g(x) ≤ h(x), then lim (x→a) g(x) = .
8. State the conditions required for the Squeeze Theorem to be applied.
9. Consider the function g(x) = x²sin(1/x). Explain how you would use the Squeeze Theorem to find lim (x→0) g(x).
10. Analyze the graph below. Identify the functions f(x), g(x), and h(x) and explain how the Squeeze Theorem applies to determine the limit of g(x) at x=0.
Explanation: