   Chapter 2.6, Problem 56E

Chapter
Section
Textbook Problem

Make a rough sketch of the curve y = xn (n an integer) for the following five cases:(i) n = 0(ii) n > 0, n odd(iii) n > 0, n even(iv) n < 0, n odd(v) n < 0, n evenThen use these sketches to find The following limits.(a) lim x → 0 + x n (b) lim x → 0 − x n (c) lim x → ∞ x n (d) lim x → − ∞ x n

(a)

To determine

To sketch: The curve y=xn for the given five cases and the values of limx0+xn by using sketches.

Explanation

Calculation:

Draw the rough graph of y=xn if n=0, n>0,n is odd, n>0,n is even and n<0,n is odd, n<0,n is even as given below.

From the sketched graph, it is observed:

(i)limx0+xn=1,  y=xn when n=0(ii)limx0+xn=0,  y=xn when n>0,n is odd(iii

(b)

To determine

To find: The values of limx0xn by using the above sketches.

(c)

To determine

To find: The values of limxxn by using the above sketches.

(d)

To determine

To find: The values of limxxn by using the above sketches.

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Find all possible real solutions of each equation in Exercises 3144. x31=0

Finite Mathematics and Applied Calculus (MindTap Course List)

II. Operating Leverage and Business Risk Once you have determined the break-even poi...

Mathematical Applications for the Management, Life, and Social Sciences

Find each difference: (2x25x2)(x2x+8)

Elementary Technical Mathematics

A sample of n = 9 scores has X = 108. What is the sample mean?

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Find if , y = sin 2t.

Study Guide for Stewart's Multivariable Calculus, 8th

True or False: n=1an converges if and only if limnan=0.

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Find each value. logaa

College Algebra (MindTap Course List)

Define content analysis and archival research.

Research Methods for the Behavioral Sciences (MindTap Course List)

Identify and describe the content of each section of an APA-style research report.

Research Methods for the Behavioral Sciences (MindTap Course List) 