← MATH 01130 · Calculus I
MATH 01130 · Limits & continuity
Squeeze theorem idea
Definition
If g(x) ≤ f(x) ≤ h(x) near a (except maybe at a) and lim g = lim h = L, then lim f = L. Used when direct algebra fails, especially with oscillating factors.
Read this
Classic: −|x| ≤ x sin(1/x) ≤ |x| → squeeze to 0 as x→0.
Also proves lim θ→0 sinθ/θ = 1 (geometric squeeze), which unlocks trig derivatives.
You must justify the inequality sandwich — not just hope.
Drill with flashcards
Flip through these until you can say the answer before revealing it.
Flashcards · 1 / 3
Click the card to flip
Try this
Attempt each problem first, then open the worked solution.
1.Prove lim x→0 x² cos(1/x) = 0 using squeeze.