Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 3: Q. 65 (page 311)

A function f dominates another function g as x → ∞ if f(x) and g(x) both grow without bound as x → ∞ and if Intuitively, f dominates g as x → ∞ if f(x) is very much larger than g(x) for very large values of x. In Exercises 65–74, use limits to determine whether u(x) dominates v(x), or v(x) dominates u(x), or neither.

u(x)=x+100,v(x)=x

Short Answer

Expert verified

limx→∞v(x)u(x)=limx→∞u(x)v(x)=1

Step by step solution

01

Step 1. Given information

u(x)=x+100,v(x)=x

02

Step 2. Calculate limx→∞u(x)v(x)

limx→∞ u(x)v(x)=limx→∞ x+100x=limx→∞ 1+100x=1+0=1

03

Step 3. Calculate limx→∞v(x)u(x)

limx→∞ v(x)u(x)=limx→∞ xx+100=limx→∞ x+100−100x+100=limx→∞ 1−100x+100=1

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Find the critical points of each function f .Then use a graphing utility to determine whether f has a local minimum, a local maximum, or neither at each of these critical point. fx=x3+x2+1

Use a sign chart for f'to determine the intervals on which each function fis increasing or decreasing. Then verify your algebraic answers with graphs from a calculator or graphing utility.

ln(x2+1)

For each graph of f in Exercises 49–52, explain why f satisfies the hypotheses of the Mean Value Theorem on the given interval [a, b] and approximate any values c ∈ (a, b) that satisfy the conclusion of the Mean Value Theorem.

Restate Rolle’s Theorem so that its conclusion has to do with tangent lines.

Find the possibility graph of its derivative f'.
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free