(a) Answer The value of f is not defined at x = 2 . Explanation Given information: The given function is f ( x ) = { x 2 − 1 , − 1 ≤ x < 0 2 x , 0 < x < 1 1 , x = 1 − 2 x + 4 , 1 < x < 2 0 , 2 < x < 3 and the graph of the function is given below: Calculation: As observed from the graph of the function, the value of the function f ( x ) at x = 2 has a breakpoint.So, the value of f ( x ) does not existat this point. Therefore, the value of f is not defined at x = 2 . (b) To determine To check: Whether the function f is continuous at x = 2 or not. Answer The function f is not continuous at x = 2 as the value of f ( 2 ) does not exist. Explanation Given information: The given function is f ( x ) = { x 2 − 1 , − 1 ≤ x < 0 2 x , 0 < x < 1 1 , x = 1 − 2 x + 4 , 1 < x < 2 0 , 2 < x < 3 and the graph of the function is given below: Calculation: As calculated in part(a), the value of f ( 2 ) does not exist. According to definition of continuity a function f ( x ) is continuous at x = a if and only if lim x → a f ( x ) = f ( a ) . Therefore, the function f is not continuous at x = 2 .

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

4th Edition

ISBN: 9780133178579

Author: Ross L. Finney

Publisher: PEARSON

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Question

Chapter 2.3, Problem 13E

(a)

To determine

To check:Whetherthe function f is defined at x=2 or not.

(a)

Expert Solution

Answer to Problem 13E

The value of f is not defined at x=2 .

Explanation of Solution

Given information:

The given function is f(x)={x2−1, −1≤x<02x, 0<x<11, x=1−2x+4, 1<x<20, 2<x<3 and the graph of the function is given below:

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter 2.3, Problem 13E , additional homework tip 1

Calculation:

As observed from the graph of the function, the value of the function f(x) at x=2 has a breakpoint.So, the value of f(x) does not existat this point.

Therefore, the value of f is not defined at x=2 .

(b)

To determine

To check:Whether the function f is continuous at x=2 or not.

(b)

Expert Solution

Answer to Problem 13E

The function f is not continuous at x=2 as the value of f(2) does not exist.

Explanation of Solution

Given information:

The given function is f(x)={x2−1, −1≤x<02x, 0<x<11, x=1−2x+4, 1<x<20, 2<x<3

and the graph of the function is given below:

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter 2.3, Problem 13E , additional homework tip 2

Calculation:

As calculated in part(a), the value of f(2) does not exist.

According to definition of continuity a function f(x) is continuous at x=a if and only if limx→af(x)=f(a) .

Therefore, the function f is not continuous at x=2 .

Chapter 2.3, Problem 12E

Chapter 2.3, Problem 14E

Chapter 2 Solutions

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

Ch. 2.1 - Prob. 1QR Ch. 2.1 - Prob. 2QR Ch. 2.1 - Prob. 3QR Ch. 2.1 - Prob. 4QR Ch. 2.1 - Prob. 5QR Ch. 2.1 - Prob. 6QR Ch. 2.1 - Prob. 7QR Ch. 2.1 - Prob. 8QR Ch. 2.1 - Prob. 9QR Ch. 2.1 - Prob. 10QR

Ch. 2.1 - Prob. 1E Ch. 2.1 - Prob. 2E Ch. 2.1 - Prob. 3E Ch. 2.1 - Prob. 4E Ch. 2.1 - Prob. 5E Ch. 2.1 - Prob. 6E Ch. 2.1 - Prob. 7E Ch. 2.1 - Prob. 8E Ch. 2.1 - Prob. 9E Ch. 2.1 - Prob. 10E Ch. 2.1 - Prob. 11E Ch. 2.1 - Prob. 12E Ch. 2.1 - Prob. 13E Ch. 2.1 - Prob. 14E Ch. 2.1 - Prob. 15E Ch. 2.1 - Prob. 16E Ch. 2.1 - Prob. 17E Ch. 2.1 - Prob. 18E Ch. 2.1 - Prob. 19E Ch. 2.1 - Prob. 20E Ch. 2.1 - Prob. 21E Ch. 2.1 - Prob. 22E Ch. 2.1 - Prob. 23E Ch. 2.1 - Prob. 24E Ch. 2.1 - Prob. 25E Ch. 2.1 - Prob. 26E Ch. 2.1 - Prob. 27E Ch. 2.1 - Prob. 28E Ch. 2.1 - Prob. 29E Ch. 2.1 - Prob. 30E Ch. 2.1 - Prob. 31E Ch. 2.1 - Prob. 32E Ch. 2.1 - Prob. 33E Ch. 2.1 - Prob. 34E Ch. 2.1 - Prob. 35E Ch. 2.1 - Prob. 36E Ch. 2.1 - Prob. 37E Ch. 2.1 - Prob. 38E Ch. 2.1 - Prob. 39E Ch. 2.1 - Prob. 40E Ch. 2.1 - Prob. 41E Ch. 2.1 - Prob. 42E Ch. 2.1 - Prob. 43E Ch. 2.1 - Prob. 44E Ch. 2.1 - Prob. 45E Ch. 2.1 - Prob. 46E Ch. 2.1 - Prob. 47E Ch. 2.1 - Prob. 48E Ch. 2.1 - Prob. 49E Ch. 2.1 - Prob. 50E Ch. 2.1 - 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