Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Question

Answered step-by-step

Which of the following functions $ f $ has a removable discontinuity at $ a $? If the discontinuity is removable, find a function $ g $ that agrees with $ f $ for $ x \neq a $ and is continuous at $ a $.

(a) $ f(x) = \dfrac{x^4 -1}{x - 1}$, $ a = 1 $(b) $ f(x) = \dfrac{x^3 - x^2 - 2x}{x - 2} $, $ a = 2 $(c) $ f(x) = [ \sin x ] $, $ a = \pi $

Video Answer

Solved by verified expert

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by Daniel Jaimes

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 5

Continuity

Limits

Derivatives

Brandon C.

January 15, 2023

For (c), isn't the limit as x --> pi ^ + equal to zero? The sine function is equal to -1 at 3pi/2 unless I'm misunderstanding something.

Missouri State University

Oregon State University

University of Michigan - Ann Arbor

University of Nottingham

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.

0:00

Which of the following fun…

01:06

13:27

08:48

12:42

01:02

Which of the following poi…

01:25

(a) find each point of dis…

03:39

Find the values of $x$ (if…

00:50

Multiple Choice Which of t…

03:44

No transcript available

View More Answers From This Book

Find Another Textbook

01:28

'The graph of f(x) is given below. At what x value(s) is f(x) not conti…

01:21

'The entire graph of the function g is shown in the figure below: Write…

01:45

"Triangle ABC is dilated by a factor of 2 with the center of dilation a…

01:44

'A graphing calculator is recommended.Find all solutions of the equatio…

02:58

'Evaluate each logarithm using properties of logarithms and the followi…

02:42

'The time t (in years) until failure of printer is exponentially distri…

02:35

'Calculate the standard deviation & of X for the probability distri…