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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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Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 5

Continuity

Limits

Derivatives

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 =

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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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The toll $ T $ charged for…

08:22

The toll $T$ charged for d…

06:50

01:59

The toll charged for drivi…

01:08

A parking lot charges $\$ …

01:06

The speed of traffic flow …

01:31

A student parking lot at a…

03:03

05:35

A car is stationary at a t…

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