Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
Bartleby Related Questions Icon

Related questions

Topic Video
Question
**Problem 6: Determining Continuity of \( r(x) \)**

Determine which values of \( C \) make the function \( r(x) \):

- (a) left-continuous,
- (b) right-continuous,
- (c) continuous.

The piecewise function \( r(x) \) is defined as:

\[
r(x) = 
\begin{cases} 
x^2 + 3 & \text{for } x < -1 \\
Cx & \text{for } -1 \leq x \leq 2 \\
-x^2 + 2 & \text{for } x > 2 
\end{cases}
\]

**Explanation:**

- The first piece \( x^2 + 3 \) defines \( r(x) \) for values of \( x \) less than -1.
- The second piece \( Cx \) defines \( r(x) \) for \( x \) between -1 and 2, inclusive.
- The third piece \(-x^2 + 2\) defines \( r(x) \) for values of \( x \) greater than 2.

To find the values of \( C \) that make the function \( r(x) \) left-continuous, right-continuous, or continuous, one must ensure the function values and limits match at the boundaries \( x = -1 \) and \( x = 2 \).
expand button
Transcribed Image Text:**Problem 6: Determining Continuity of \( r(x) \)** Determine which values of \( C \) make the function \( r(x) \): - (a) left-continuous, - (b) right-continuous, - (c) continuous. The piecewise function \( r(x) \) is defined as: \[ r(x) = \begin{cases} x^2 + 3 & \text{for } x < -1 \\ Cx & \text{for } -1 \leq x \leq 2 \\ -x^2 + 2 & \text{for } x > 2 \end{cases} \] **Explanation:** - The first piece \( x^2 + 3 \) defines \( r(x) \) for values of \( x \) less than -1. - The second piece \( Cx \) defines \( r(x) \) for \( x \) between -1 and 2, inclusive. - The third piece \(-x^2 + 2\) defines \( r(x) \) for values of \( x \) greater than 2. To find the values of \( C \) that make the function \( r(x) \) left-continuous, right-continuous, or continuous, one must ensure the function values and limits match at the boundaries \( x = -1 \) and \( x = 2 \).
Expert Solution
Check Mark
Knowledge Booster
Background pattern image
Calculus
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Text book image
Calculus: Early Transcendentals
Calculus
ISBN:9781285741550
Author:James Stewart
Publisher:Cengage Learning
Text book image
Thomas' Calculus (14th Edition)
Calculus
ISBN:9780134438986
Author:Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:PEARSON
Text book image
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:9780134763644
Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:PEARSON
Text book image
Calculus: Early Transcendentals
Calculus
ISBN:9781319050740
Author:Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:W. H. Freeman
Text book image
Precalculus
Calculus
ISBN:9780135189405
Author:Michael Sullivan
Publisher:PEARSON
Text book image
Calculus: Early Transcendental Functions
Calculus
ISBN:9781337552516
Author:Ron Larson, Bruce H. Edwards
Publisher:Cengage Learning