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

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01:18

Daniel Jaimes

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 5

Continuity

Limits

Derivatives

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

Ceazar V.

March 24, 2021

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

Missouri State University

Harvey Mudd College

Baylor University

Idaho State University

Lectures

04:40

In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

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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.

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