by Barney Wolford
Dive into the fascinating world of calculus with our Squeeze Theorem Quiz! This quiz will challenge your understanding of how the Squeeze Theorem is used to find limits of functions. Sharpen your skills and see how well you can apply this essential mathematical principle.
We recommend that you do not leave the page that you are taking this quiz in. Stay honest 🙂
Squeeze Theorem Quiz Questions Overview
1. What is another name for the Squeeze Theorem?
Sandwich Theorem
Pinching Theorem
Compression Theorem
All of the above
2. What is the primary use of the Squeeze Theorem?
To find the derivative of a function
To determine the limit of a function
To solve differential equations
To integrate a function
3. Which of the following conditions must be met for the Squeeze Theorem to be applicable?
The functions must be continuous
The functions must be differentiable
The functions must be bounded
The functions must have the same limit at a point
4. In the Squeeze Theorem, if f(x) ≤ g(x) ≤ h(x) for all x in an interval around c, and lim(x→c) f(x) = lim(x→c) h(x) = L, what can be concluded?
lim(x→c) g(x) = 0
lim(x→c) g(x) = L
lim(x→c) g(x) = ∞
lim(x→c) g(x) does not exist
5. Which of the following is an example of a function that can be evaluated using the Squeeze Theorem?
sin(x)/x as x approaches 0
cos(x) as x approaches 0
tan(x) as x approaches π/2
e^x as x approaches ∞
6. What is the limit of (x^2 * sin(1/x)) as x approaches 0?
0
1
∞
Does not exist
7. Which of the following inequalities is used in the Squeeze Theorem?
f(x) < g(x) < h(x)
f(x) ≤ g(x) ≤ h(x)
f(x) = g(x) = h(x)
f(x) > g(x) > h(x)
8. If f(x) = x^2 and h(x) = -x^2, what is the limit of f(x) * sin(1/x) as x approaches 0?
0
1
∞
Does not exist
9. Which of the following is NOT a requirement for the Squeeze Theorem?
The functions must be continuous
The functions must have the same limit at a point
The functions must be defined in an interval around the point
One function must be less than or equal to the other
10. What is the limit of (x * cos(1/x)) as x approaches 0?
0
1
∞
Does not exist
11. Which of the following is an appropriate bounding function for sin(x)/x as x approaches 0?
1/x
x
1
x^2
12. What is the limit of (x^2 * cos(1/x)) as x approaches 0?
0
1
∞
Does not exist
13. In the Squeeze Theorem, if f(x) ≤ g(x) ≤ h(x) and lim(x→c) f(x) = lim(x→c) h(x) = L, which of the following is true?
g(x) is undefined at x = c
g(x) has no limit as x approaches c
g(x) approaches L as x approaches c
f(x) and h(x) have different limits
14. What is the limit of (x * sin(1/x)) as x approaches 0?
0
1
∞
Does not exist
We recommend that you do not leave the page that you are taking this quiz in. Stay honest 🙂
