Calculus: Graphical, Numerical, Algebraic

3rd Edition

ISBN: 9780133688399

Author: Finney, Ross L.

Publisher: Pearson/Prentice Hall

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topic…

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Question

Chapter 3.2, Problem 8E

(a)

To determine

The domain points of the given function appear to be differentiable.

(a)

Expert Solution

Answer to Problem 8E

The required domain points of the given function appears to be differentiable is [−2,−1)∪(−1,0)∪(0,2)∪(2,3] .

Explanation of Solution

Given information:

The given function is: y=f(x) .

And, the domain points is D:−2≤x≤3

Calculus: Graphical, Numerical, Algebraic, Chapter 3.2, Problem 8E , additional homework tip 1

The given function is: y=f(x) .and the domain points is D:−2≤x≤3 .

Since, from the figure it is seen that the function y=f(x) has discontinuities point at x=0 and x=2 .

Also, from the figure it is seen that the function y=f(x) has vertical tangents at x=−1 .

Thus, the function y=f(x) is differentiable at all points in its domain except x=−1,x=0 and x=2 respectively.

Hence, the required domain of the function appears to be differentiable is [−2,−1)∪(−1,0)∪(0,2)∪(2,3] .

(b)

To determine

The domain points of the given function appear to be continuous but not differentiable.

(b)

Expert Solution

Answer to Problem 8E

The required domain of the given function appears to be continuous but not differentiable is x=−1 .

Explanation of Solution

Given information:

The given function is: y=f(x) .

And, the domain points is D:−2≤x≤3

Calculus: Graphical, Numerical, Algebraic, Chapter 3.2, Problem 8E , additional homework tip 2

The given function is y=f(x) .and the domain points is D:−2≤x≤3 .

From the results (a) it is seen that the function y=f(x) is differentiable at all points in its domain except x=−1 .

Since, the given function has discontinuities at x=0 and x=2 ..

Also, the given function y=f(x) has vertical tangents at x=−1 .

Thus, the given function y=f(x) is continuous but not differentiable at x=−1

Hence, the required domain of the function whether the function appears to be continuous but not differentiable is x=−1 .

(c)

To determine

The domain of the given function appear neither continuous nor differentiable.

(c)

Expert Solution

Answer to Problem 8E

The required domain of the given function appears to be neither continuous nor differentiable at x=0 and x=2 .

Explanation of Solution

Given information:

The given function is: y=f(x) .

And, the domain points is D:−2≤x≤3

Calculus: Graphical, Numerical, Algebraic, Chapter 3.2, Problem 8E , additional homework tip 3

The given function is: y=f(x) .and the domain points is D:−2≤x≤3 .

From the results (a) the function has discontinuities at x=0 and at x=2 , therefore the given function is also not differentiable at x=0 and at x=2 .

Hence, at x=0 and x=2 the given function appears neither continuous nor differentiable.

Chapter 3.2, Problem 7E

Chapter 3.2, Problem 9E

Chapter 3 Solutions

Calculus: Graphical, Numerical, Algebraic

Ch. 3.1 - Prob. 1QR Ch. 3.1 - Prob. 2QR Ch. 3.1 - Prob. 3QR Ch. 3.1 - Prob. 4QR Ch. 3.1 - Prob. 5QR Ch. 3.1 - Prob. 6QR Ch. 3.1 - Prob. 7QR Ch. 3.1 - Prob. 8QR Ch. 3.1 - Prob. 9QR Ch. 3.1 - Prob. 10QR

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