Squeeze Theorem Practice
A worksheet for Grade 10 students to practice applying the Squeeze Theorem to determine limits of functions.
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Squeeze Theorem Practice
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Read each question carefully and apply the Squeeze Theorem to find the limit of the given functions. Show all your work.
1. If $4x - 9 \le f(x) \le x^2 - 4x + 7$ for $x \ge 0$, find $\lim_{x \to 4} f(x)$.
2. Given that $1 - \frac{x^2}{4} \le u(x) \le 1 + \frac{x^2}{2}$ for all $x \ne 0$, evaluate $\lim_{x \to 0} u(x)$.
3. The Squeeze Theorem states that if $g(x) \le f(x) \le h(x)$ for all $x$ in an open interval containing $c$, except possibly at $c$ itself, and if $\lim_{x \to c} g(x) = L$ and $\lim_{x \to c} h(x) = L$, then $\lim_{x \to c} f(x) = \text{ }$.
4. Which of the following conditions is necessary to apply the Squeeze Theorem?
The function $f(x)$ must be continuous.
The bounding functions $g(x)$ and $h(x)$ must have the same limit.
The function $f(x)$ must be differentiable.
The bounding functions $g(x)$ and $h(x)$ must be linear.
5. The Squeeze Theorem can only be used when the limits of the bounding functions are equal to zero.
True
False
6. Use the Squeeze Theorem to show that $\lim_{x \to 0} x^2 \sin(\frac{1}{x}) = 0$.