PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
8th Edition
ISBN: 9781337904285
Author: Larson
Publisher: CENGAGE L
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Chapter 11.1, Problem 22E
To determine

To find: The value of the limx0xtanx using table feature of a graphing utility. Also confirm your result graphically.

Expert Solution & Answer
Check Mark

Answer to Problem 22E

The value of the limits is limx0xtanx=1

Explanation of Solution

Given information:

Given expression of limit as limx0xtanx

Let, f(x)=xtanx

The value of the function at x=0.1 is,

  f(0.1)=(0.1)tan(0.1)=0.10.1003=0.997

The value of the function at x=0.01 is,

  f(0.01)=(0.01)tan(0.01)=0.010.0100003=0.99997

The value of the function at x=0.001 is,

  f(0.001)=(0.001)tan(0.001)=0.9999997

The value of the function at x=0 is,

  f(0)=(0)tan(0)=00=undefined

The value of the function at x=0.1 is,

  f(0.1)=(0.1)tan(0.1)=0.10.100335=0.99666

The value of the function at x=0.01 is,

  f(0.01)=(0.01)tan(0.01)=0.010.010000335=0.999966

The value of the function at x=0.001 is,

  f(0.001)=(0.001)tan(0.001)=0.0010.00100000033=0.99999967

Hence, the complete table is,

  x0.10.010.00100.10.010.001f(x)0.9970.999970.9999997undefined0.996660.9999660.99999967

The value of the limit is, limx0xtanx=1

Graph of the function can be drawn as,

  PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 11.1, Problem 22E

From the graph it is clear that limx0xtanx=1

Chapter 11 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

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