Finite Math Examples

Prove that a Root is on the Interval
The Intermediate Value Theorem states that, if is a real-valued continuous function on the interval , and is a number between and , then there is a contained in the interval such that .
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Interval Notation:
Set-Builder Notation:
Subtract from .
Subtract from .

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Rewrite the equation as .
Add to both sides of the equation.
The Intermediate Value Theorem states that there is a root on the interval because is a continuous function on .
The roots on the interval are located at .
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