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Squeeze Theorem Visualizer
AP Calculus AB · Unit 1 Limits
Learning Objectives
Apply the Squeeze Theorem to evaluate limits
Identify bounding functions g(x) ≤ f(x) ≤ h(x)
Prove lim x→0 (sin x)/x = 1 using squeeze
Visualize convergence of bounds at the limit point
Theorem
If
g(x) ≤ f(x) ≤ h(x)
near x=a, and
lim g(x) = lim h(x) = L as x→a,
then
lim f(x) = L
as x→a.
The function is "squeezed" between two bounds that converge to the same limit.
Tags
squeeze theorem
limits
sin x / x
bounds
EXAMPLE
f(x) = x²sin(1/x), x→0
f(x) = sin(x)/x, x→0
f(x) = x·cos(1/x), x→0
f(x) = (1−cos x)/x², x→0
Zoom Level
1.0
Limit
0
At x→
0