The Squeeze Theorem

Drag the yellow handle to squeeze the chaotic blue function between the red and green bounds.

Squeezed! The limit must be 0.

Build the Bounds

Let's prove algebraically.

Step 1: Start with known bounds

Multiply all parts by what to get in the middle?

Step 2: The Squeezed Function

As , what do the outer bounds ( and ) approach?

The Special Limit

Slide towards 0 to evaluate

x = 2 x → 0
x
{{ s3.xVal.toFixed(4) }}
f(x)
{{ s3.fxVal.toFixed(4) }}

Balance the Equation

Drag the constants to rewrite the limit using

{{ s4.zones.z1.val }}
{{ s4.zones.z2.val }}
×
{{ s4.zones.z3.val }}

Drag constants to boxes

{{ item.val }}

Mastered!

You've successfully used the Squeeze Theorem and algebraic manipulation to solve complex limits.