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# If $f$ is continuous on $(-\infty, \infty)$, what can you say about its graph?

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Limits

Derivatives

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CV

Ceazar V.

March 24, 2021

From the graph of shown, state the intervals on which is continuous.

CV

Ceazar V.

March 24, 2021

ss

Sudhakar S.

May 7, 2021

Use the Intermediate Value Theorem to show that there is a root of the given equation in the specific interva

ss

Sudhakar S.

May 7, 2021

ss

Sudhakar S.

May 7, 2021

ss

Sudhakar S.

May 7, 2021

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

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### Video Transcript

I are X axis is continuous everywhere from X negative infinity. All the way to excess positive infinity. There's a few things that we could say about the function of X. Uh First of all, it is defined if it's continuous on the entire X axis and it is clearly defined on the entire X axis. And also such first thing that we can claim. 2nd thing we can clean is that the limit of F of X as X approaches any number A on the X axis exists. So if F is continuous on the entire uh, X access, then it's defined everywhere on the X axis. And more importantly, the limit of the function exists as X approaches any number A belonging on the X axis. Okay.

Temple University

#### Topics

Limits

Derivatives

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

Lectures

Join Bootcamp