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 11.4, Problem 34E

(a)

To determine

To calculate:

Complete the table and limit for the given function.

(a)

Expert Solution
Check Mark

Answer to Problem 34E

Limit of the function is y=0

    x100101102103104105106
    f(x)20.970.99970.9999970.999999970.99999999970.999999999997

Explanation of Solution

Given information:

  f(x)=2x+1x21

    x100101102103104105106
    f(x)

Calculation:

For completing the table of the sequence,

Consider the given functions,

  f(x)=2x+1x21

The value of the function f(x)=2x+1x21 for x=100=1 ,

  f(x)=2x+1x21=2(1)+1(1)21=30

The value of the function f(x)=2x+1x21 for x=10 ,

  f(x)=2x+1x21=2(10)+1(10)21=2199=0.212121

The value of the function f(x)=2x+1x21 for x=102 ,

  f(x)=2x+1x21=2(100)+1(100)21=2019999=0.02102

The value of the function f(x)=2x+1x21 for x=103 ,

  f(x)=2x+1x21=2(1000)+1(1000)21=2001999999=0.0021001

The value of the function f(x)=2x+1x21 for x=104 ,

  f(x)=2x+1x21=2(10000)+1(10000)21=20001999999999=0.000210001

The value of the function f(x)=2x+1x21 for x=105 ,

  f(x)=2x+1x21=2(100000)+1(100000)21=200001999999999=0.00002

The value of the function f(x)=2x+1x21 for x=106 ,

  f(x)=2x+1x21=2(1000000)+1(1000000)21=2000000199999999999=0.000002

For making a table above data is used,

    x100101102103104105106
    f(x)Error 0.2121210.021020.0020010.000200010.000020.000002

(b)

To determine

To graph:

Estimate the limit by using graph.

(b)

Expert Solution
Check Mark

Explanation of Solution

Given information:

  f(x)=2x+1x21

Graph:

  PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 11.4, Problem 34E

Interpretation:

Thus, from the table in part (a) it is observed that x approaches at infinity the function f(x) get closure to 0 .

Hence, the required graph of the function and limit showing graphically is 0 .

(c)

To determine

To calculate:

Limit of the given function algebraically..

(c)

Expert Solution
Check Mark

Answer to Problem 34E

Limit of the function algebraically is limxf(x)=0

Explanation of Solution

Given information:

  f(x)=2x+1x21

Calculation:

For finding out the limit of the given function algebraically,

  f(x)=2x+1x21

Limit of the function f(x) as x approaches at infinity is

  limxf(x)=limx2x+1x21=limx2x(1+12x)x2(112x)=limx2(1+12x)x(11x2)=2(1+12())()(11()2)=0

Hence, the required limit of the function algebraically is limxf(x)=0

Chapter 11 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

Ch. 11.1 - Prob. 11ECh. 11.1 - Prob. 12ECh. 11.1 - Prob. 13ECh. 11.1 - Prob. 14ECh. 11.1 - Prob. 15ECh. 11.1 - Prob. 16ECh. 11.1 - Prob. 17ECh. 11.1 - Prob. 18ECh. 11.1 - Prob. 19ECh. 11.1 - Prob. 20ECh. 11.1 - Prob. 21ECh. 11.1 - Prob. 22ECh. 11.1 - Prob. 23ECh. 11.1 - Prob. 24ECh. 11.1 - Prob. 25ECh. 11.1 - Prob. 26ECh. 11.1 - Prob. 27ECh. 11.1 - Prob. 28ECh. 11.1 - Prob. 29ECh. 11.1 - Prob. 30ECh. 11.1 - Prob. 31ECh. 11.1 - Prob. 32ECh. 11.1 - Prob. 33ECh. 11.1 - Prob. 34ECh. 11.1 - Prob. 35ECh. 11.1 - Prob. 36ECh. 11.1 - Prob. 37ECh. 11.1 - Prob. 38ECh. 11.1 - Prob. 39ECh. 11.1 - Prob. 40ECh. 11.1 - Prob. 41ECh. 11.1 - Prob. 42ECh. 11.1 - Prob. 43ECh. 11.1 - Prob. 44ECh. 11.1 - Prob. 45ECh. 11.1 - Prob. 46ECh. 11.1 - Prob. 47ECh. 11.1 - Prob. 48ECh. 11.1 - Prob. 49ECh. 11.1 - Prob. 50ECh. 11.1 - Prob. 51ECh. 11.1 - Prob. 52ECh. 11.1 - Prob. 53ECh. 11.1 - Prob. 54ECh. 11.1 - Prob. 55ECh. 11.1 - Prob. 56ECh. 11.1 - Prob. 57ECh. 11.1 - Prob. 58ECh. 11.1 - Prob. 59ECh. 11.1 - Prob. 60ECh. 11.1 - Prob. 61ECh. 11.1 - Prob. 62ECh. 11.1 - Prob. 63ECh. 11.1 - Prob. 64ECh. 11.1 - Prob. 65ECh. 11.1 - Prob. 66ECh. 11.1 - Prob. 67ECh. 11.1 - Prob. 68ECh. 11.1 - Prob. 69ECh. 11.1 - Prob. 70ECh. 11.1 - Prob. 71ECh. 11.1 - Prob. 72ECh. 11.1 - Prob. 73ECh. 11.1 - Prob. 74ECh. 11.1 - Prob. 75ECh. 11.1 - Prob. 76ECh. 11.1 - Prob. 77ECh. 11.1 - Prob. 78ECh. 11.1 - Prob. 79ECh. 11.1 - Prob. 80ECh. 11.1 - Prob. 81ECh. 11.1 - Prob. 82ECh. 11.1 - Prob. 83ECh. 11.1 - Prob. 84ECh. 11.1 - Prob. 85ECh. 11.1 - Prob. 86ECh. 11.2 - Prob. 1ECh. 11.2 - Prob. 2ECh. 11.2 - Prob. 3ECh. 11.2 - Prob. 4ECh. 11.2 - Prob. 5ECh. 11.2 - Prob. 6ECh. 11.2 - Prob. 7ECh. 11.2 - Prob. 8ECh. 11.2 - Prob. 9ECh. 11.2 - Prob. 10ECh. 11.2 - Prob. 11ECh. 11.2 - Prob. 12ECh. 11.2 - Prob. 13ECh. 11.2 - Prob. 14ECh. 11.2 - Prob. 15ECh. 11.2 - Prob. 16ECh. 11.2 - Prob. 17ECh. 11.2 - Prob. 18ECh. 11.2 - Prob. 19ECh. 11.2 - Prob. 20ECh. 11.2 - Prob. 21ECh. 11.2 - Prob. 22ECh. 11.2 - Prob. 23ECh. 11.2 - Prob. 24ECh. 11.2 - Prob. 25ECh. 11.2 - Prob. 26ECh. 11.2 - Prob. 27ECh. 11.2 - Prob. 28ECh. 11.2 - Prob. 29ECh. 11.2 - Prob. 30ECh. 11.2 - Prob. 31ECh. 11.2 - Prob. 32ECh. 11.2 - Prob. 33ECh. 11.2 - Prob. 34ECh. 11.2 - Prob. 35ECh. 11.2 - Prob. 36ECh. 11.2 - Prob. 37ECh. 11.2 - Prob. 38ECh. 11.2 - Prob. 39ECh. 11.2 - Prob. 40ECh. 11.2 - Prob. 41ECh. 11.2 - Prob. 42ECh. 11.2 - Prob. 43ECh. 11.2 - Prob. 44ECh. 11.2 - Prob. 45ECh. 11.2 - Prob. 46ECh. 11.2 - Prob. 47ECh. 11.2 - Prob. 48ECh. 11.2 - Prob. 49ECh. 11.2 - Prob. 50ECh. 11.2 - Prob. 51ECh. 11.2 - Prob. 52ECh. 11.2 - Prob. 53ECh. 11.2 - Prob. 54ECh. 11.2 - Prob. 55ECh. 11.2 - Prob. 56ECh. 11.2 - Prob. 57ECh. 11.2 - Prob. 58ECh. 11.2 - Prob. 59ECh. 11.2 - Prob. 60ECh. 11.2 - Prob. 61ECh. 11.2 - Prob. 62ECh. 11.2 - Prob. 63ECh. 11.2 - Prob. 64ECh. 11.2 - Prob. 65ECh. 11.2 - Prob. 66ECh. 11.2 - Prob. 67ECh. 11.2 - Prob. 68ECh. 11.2 - Prob. 69ECh. 11.2 - Prob. 70ECh. 11.2 - Prob. 71ECh. 11.2 - Prob. 72ECh. 11.2 - Prob. 73ECh. 11.2 - Prob. 74ECh. 11.2 - Prob. 75ECh. 11.2 - 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Prob. 11ECh. 11.4 - Prob. 12ECh. 11.4 - Prob. 13ECh. 11.4 - Prob. 14ECh. 11.4 - Prob. 15ECh. 11.4 - Prob. 16ECh. 11.4 - Prob. 17ECh. 11.4 - Prob. 18ECh. 11.4 - Prob. 19ECh. 11.4 - Prob. 20ECh. 11.4 - Prob. 21ECh. 11.4 - Prob. 22ECh. 11.4 - Prob. 23ECh. 11.4 - Prob. 24ECh. 11.4 - Prob. 25ECh. 11.4 - Prob. 26ECh. 11.4 - Prob. 27ECh. 11.4 - Prob. 28ECh. 11.4 - Prob. 29ECh. 11.4 - Prob. 30ECh. 11.4 - Prob. 31ECh. 11.4 - Prob. 32ECh. 11.4 - Prob. 33ECh. 11.4 - Prob. 34ECh. 11.4 - Prob. 35ECh. 11.4 - Prob. 36ECh. 11.4 - Prob. 37ECh. 11.4 - Prob. 38ECh. 11.4 - Prob. 39ECh. 11.4 - Prob. 40ECh. 11.4 - Prob. 41ECh. 11.4 - Prob. 42ECh. 11.4 - Prob. 43ECh. 11.4 - Prob. 44ECh. 11.4 - Prob. 45ECh. 11.4 - Prob. 46ECh. 11.4 - Prob. 47ECh. 11.4 - Prob. 48ECh. 11.4 - Prob. 49ECh. 11.4 - Prob. 50ECh. 11.4 - Prob. 51ECh. 11.4 - Prob. 52ECh. 11.4 - Prob. 53ECh. 11.4 - Prob. 54ECh. 11.4 - Prob. 55ECh. 11.4 - Prob. 56ECh. 11.4 - Prob. 57ECh. 11.4 - Prob. 58ECh. 11.4 - Prob. 59ECh. 11.4 - Prob. 60ECh. 11.4 - Prob. 61ECh. 11.4 - Prob. 62ECh. 11.4 - Prob. 63ECh. 11.4 - Prob. 64ECh. 11.4 - Prob. 65ECh. 11.4 - Prob. 66ECh. 11.4 - Prob. 67ECh. 11.4 - Prob. 68ECh. 11.4 - Prob. 69ECh. 11.4 - Prob. 70ECh. 11.4 - Prob. 71ECh. 11.4 - Prob. 72ECh. 11.4 - Prob. 73ECh. 11.4 - Prob. 74ECh. 11.4 - Prob. 75ECh. 11.4 - Prob. 76ECh. 11.5 - Prob. 1ECh. 11.5 - Prob. 2ECh. 11.5 - Prob. 3ECh. 11.5 - Prob. 4ECh. 11.5 - Prob. 5ECh. 11.5 - Prob. 6ECh. 11.5 - Prob. 7ECh. 11.5 - Prob. 8ECh. 11.5 - Prob. 9ECh. 11.5 - Prob. 10ECh. 11.5 - Prob. 11ECh. 11.5 - Prob. 12ECh. 11.5 - Prob. 13ECh. 11.5 - Prob. 14ECh. 11.5 - Prob. 15ECh. 11.5 - Prob. 16ECh. 11.5 - Prob. 17ECh. 11.5 - Prob. 18ECh. 11.5 - Prob. 19ECh. 11.5 - Prob. 20ECh. 11.5 - Prob. 21ECh. 11.5 - Prob. 22ECh. 11.5 - Prob. 23ECh. 11.5 - Prob. 24ECh. 11.5 - Prob. 25ECh. 11.5 - Prob. 26ECh. 11.5 - Prob. 27ECh. 11.5 - Prob. 28ECh. 11.5 - Prob. 29ECh. 11.5 - Prob. 30ECh. 11.5 - Prob. 31ECh. 11.5 - Prob. 32ECh. 11.5 - Prob. 33ECh. 11.5 - Prob. 34ECh. 11.5 - Prob. 35ECh. 11.5 - Prob. 36ECh. 11.5 - Prob. 37ECh. 11.5 - Prob. 38ECh. 11.5 - Prob. 39ECh. 11.5 - Prob. 40ECh. 11.5 - Prob. 41ECh. 11.5 - Prob. 42ECh. 11.5 - Prob. 43ECh. 11.5 - Prob. 44ECh. 11 - Prob. 1CRCh. 11 - Prob. 2CRCh. 11 - Prob. 3CRCh. 11 - Prob. 4CRCh. 11 - Prob. 5CRCh. 11 - Prob. 6CRCh. 11 - Prob. 7CRCh. 11 - Prob. 8CRCh. 11 - Prob. 9CRCh. 11 - Prob. 10CRCh. 11 - Prob. 11CRCh. 11 - Prob. 12CRCh. 11 - Prob. 13CRCh. 11 - Prob. 14CRCh. 11 - Prob. 15CRCh. 11 - Prob. 16CRCh. 11 - Prob. 17CRCh. 11 - Prob. 18CRCh. 11 - Prob. 19CRCh. 11 - Prob. 20CRCh. 11 - Prob. 21CRCh. 11 - Prob. 22CRCh. 11 - Prob. 23CRCh. 11 - Prob. 24CRCh. 11 - Prob. 25CRCh. 11 - Prob. 26CRCh. 11 - Prob. 27CRCh. 11 - Prob. 28CRCh. 11 - Prob. 29CRCh. 11 - Prob. 30CRCh. 11 - Prob. 31CRCh. 11 - Prob. 32CRCh. 11 - Prob. 33CRCh. 11 - Prob. 34CRCh. 11 - Prob. 35CRCh. 11 - Prob. 36CRCh. 11 - Prob. 37CRCh. 11 - Prob. 38CRCh. 11 - Prob. 39CRCh. 11 - Prob. 40CRCh. 11 - Prob. 41CRCh. 11 - Prob. 42CRCh. 11 - Prob. 43CRCh. 11 - Prob. 44CRCh. 11 - Prob. 45CRCh. 11 - Prob. 46CRCh. 11 - Prob. 47CRCh. 11 - Prob. 48CRCh. 11 - Prob. 49CRCh. 11 - Prob. 50CRCh. 11 - Prob. 51CRCh. 11 - Prob. 52CRCh. 11 - Prob. 53CRCh. 11 - Prob. 54CRCh. 11 - Prob. 55CRCh. 11 - Prob. 56CRCh. 11 - Prob. 57CRCh. 11 - Prob. 58CRCh. 11 - Prob. 59CRCh. 11 - Prob. 60CRCh. 11 - Prob. 61CRCh. 11 - Prob. 62CRCh. 11 - Prob. 63CRCh. 11 - Prob. 64CRCh. 11 - Prob. 65CRCh. 11 - Prob. 66CRCh. 11 - Prob. 67CRCh. 11 - Prob. 68CRCh. 11 - Prob. 69CRCh. 11 - Prob. 70CRCh. 11 - Prob. 71CRCh. 11 - Prob. 72CRCh. 11 - Prob. 73CRCh. 11 - Prob. 74CRCh. 11 - Prob. 75CRCh. 11 - Prob. 76CRCh. 11 - Prob. 77CRCh. 11 - Prob. 78CRCh. 11 - Prob. 79CRCh. 11 - Prob. 80CRCh. 11 - Prob. 81CRCh. 11 - Prob. 82CRCh. 11 - Prob. 83CRCh. 11 - Prob. 84CRCh. 11 - Prob. 85CRCh. 11 - Prob. 86CRCh. 11 - Prob. 87CRCh. 11 - Prob. 88CRCh. 11 - Prob. 89CRCh. 11 - Prob. 90CRCh. 11 - Prob. 91CRCh. 11 - Prob. 92CRCh. 11 - Prob. 93CRCh. 11 - Prob. 94CRCh. 11 - Prob. 95CRCh. 11 - Prob. 96CRCh. 11 - Prob. 97CRCh. 11 - 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