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Problem

Explain why each function is continuous or discon…

07:17

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Problem 9 Easy Difficulty

The toll $ T $ charged for driving on a certain stretch of a toll road is 5 dollars except during rush hours (between 7 AM and 10 AM and between 4 PM and 7 PM) when the toll is 7 dollars.
(a) Sketch a graph of $ T $ as a function of the time $ t $, measured in hours past midnight.
(b) Discuss the discontinuities of this function and their significance to someone who uses the road.


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Related Courses

Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 2

Limits and Derivatives

Section 5

Continuity

Related Topics

Limits

Derivatives

Discussion

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SH

Samira H.

June 23, 2021

Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a. f(x) = x + 3x4 5 , a = ?1 lim x??1 f(x) = lim x??1 5 = lim x??1 5 by the power law =

Top Calculus 1 / AB Educators
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Lectures

Video Thumbnail

04:40

Limits - Intro

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.

Video Thumbnail

04:40

Derivatives - Intro

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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Watch More Solved Questions in Chapter 2

Problem 1
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Problem 16
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Problem 33
Problem 34
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Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
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Problem 43
Problem 44
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
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Problem 53
Problem 54
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Calculus: Early Transcendentals

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Related Topics

Limits

Derivatives

Top Calculus 1 / AB Educators
Catherine Ross

Missouri State University

Anna Marie Vagnozzi

Campbell University

Heather Zimmers

Oregon State University

Michael Jacobsen

Idaho State University

Calculus 1 / AB Courses

Lectures

Video Thumbnail

04:40

Limits - Intro

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.

Video Thumbnail

04:40

Derivatives - Intro

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.

Join Course
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