BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 1.6, Problem 46E
To determine

To compare: The graphs of f(x)=x0.1 and g(x)=lnx and find the point where graph of g surpasses graph of f.

Expert Solution

Answer to Problem 46E

The curve of f(x) surpasses the curve of g(x) at the point x=3.431×1015 .

Explanation of Solution

Graphs:

Use online graphing calculator and draw the graph of the functions f(x)=x0.1 and g(x)=lnx as shown in the Figure1,

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 1.6, Problem 46E , additional homework tip  1

From Figure1, observe that f(x) and g(x) has only one intersection point (3.05973,1.11833) .and if 0<x<3.05973 , then f(x)g(x) .

Zoom in the graph in Figure 1 and draw the graph of the given function as shown in below Figure 2,

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 1.6, Problem 46E , additional homework tip  2

From Figure2, observe that the curve of f(x) approaches g(x) when x is large.

By zooming Figure2, draw the graph of the function as shown in below Figure 3,

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 1.6, Problem 46E , additional homework tip  3

From Figure3, observe that f(x) is equal to g(x) at point (3.431×1015,35.772) .

Therefore, the curve f(x) surpasses the curve g(x) is at the point x=3.431×1015 .

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