# Intermediate Value Theorem Problems And Solutions Pdf

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The Real Number System. Convergence of a Sequence, Monotone Sequences. Cauchy Criterion, Bolzano - Weierstrass Theorem. Continuity and Limits.

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Many functions have the property that their graphs can be traced with a pencil without lifting the pencil from the page. Normally, such functions are called continuous. Other functions have points at which a break in the graph occurs, but satisfy this property over intervals contained in their domains. They are continuous on these intervals and are said to have a discontinuity at a point where a break occurs. We begin our investigation of continuity by exploring what it means for a function to have continuity at a point.

## Intermediate Value Theorem

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## 1.6: Continuity and the Intermediate Value Theorem

Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up. I have been stuck on this Real Analysis problem for hours and am just totally clueless- I am sure it is some application of the Intermediate Value Theorem-. Let us assume the first case, the other case being handled similarly. Thus no such function exists.

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If you're seeing this message, it means we're having trouble loading external resources on our website. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Donate Login Sign up Search for courses, skills, and videos. Intermediate value theorem. Worked example: using the intermediate value theorem.

The Intermediate Value Theorem is one of the most important theorems in Introductory Calculus, and it forms the basis for proofs of many results in subsequent and advanced Mathematics courses. Generally speaking, the Intermediate Value Theorem applies to continuous functions and is used to prove that equations, both algebraic and transcendental , are solvable. The formal statement of this theorem together with an illustration of the theorem follow. All functions are assumed to be real-valued.

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Can the same be said for the function:?

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Continuous is a special term with an exact definition in calculus, but here we will use this simplified definition:.

It represents the idea that the graph of a continuous function on a closed interval can be drawn without lifting a pencil from the paper.