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Chapter 3: Q. 70 (page 311)

A function f dominates another function g as x鈫�鈭�if fx,gxboth grow without bound as x鈫�鈭�and if data-custom-editor="chemistry" limx鈫�鈭�fxgx=鈭�.

Intuitively, f dominates gas x鈫�鈭�if fxis very much larger than gxfor very large values of x. Use limits to determine whether uxdominates data-custom-editor="chemistry" vxor vxdominates uxor neither.

ux=x10+3,vx=10x+3

Short Answer

Expert verified

The function uxdominates vxso localid="1648749438712" limx鈫�鈭�x10+310x+3=鈭�.

Step by step solution

01

Step 1. Given information.

Consider the given question,

ux=x10+3,vx=10x+3

02

Step 2. Use the limits.

Using the limits,

limx鈫�鈭�uxvx=limx鈫�鈭�x10+310x+3

Asx10>10x,

localid="1648749428944" limx鈫�鈭�x10+310x+3=鈭�

Again, localid="1648749419242" limx鈫�鈭�vxux=limx鈫�鈭�10x+3x10+3

As x10>10x,

localid="1648749422931" limx鈫�鈭�10x+3x10+3=0

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Most popular questions from this chapter

The cost of manufacturing a container for frozen orange juice is C(h)=h2-7.4h+13.7cents, where his the height of the container in inches. Your boss claims that the containers will be the cheapest to make if they are 4inches tall. Use Theorem 3.3 to quickly show that he is wrong.

Sketch careful, labeled graphs of each function f in Exercises 63鈥�82 by hand, without consulting a calculator or graphing utility. As part of your work, make sign charts for the signs, roots, and undefined points of f,f',andf'', and examine any relevant limits so that you can describe all key points and behaviors of f.

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For each set of sign charts in Exercises 53鈥�62, sketch a possible graph of f.

Explain the difference between two antiderivatives of the function.

Find the possibility graph of its derivative f'.
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