a. Answer The approximate limit by using a graphing utility to graph the given function does not exist. Explanation Given: lim x → 2 x 4 − 1 x 4 − 3 x 2 − 4 The above graph is the graphical representation of the given function with the limits lim x → 2 x 4 − 1 x 4 − 3 x 2 − 4 . From the graph we observe the limit does not exist. Thus we can find the limit using graphing utility. b. To determine To find: To numerically approximate the limit by using the table feature of the graphing utility to create a table. Answer The numerically approximate limit using a table from the graph does not exist. Explanation Given: lim x → 2 x 4 − 1 x 4 − 3 x 2 − 4 From the graph we can create a table, x f(x) 1.9 -6.692 1.99 -74.188 1.999 -749.188 2 Error 2.001 750.813 2.01 75.813 2.1 8.317 Therefore we can conclude that numerically the limit of the given function does not exist. c. To determine To find: To algebraically evaluate the limit by using the appropriate techniques. Answer By evaluating the given limit algebraically the limit does not exist. Explanation Given: lim x → 2 x 4 − 1 x 4 − 3 x 2 − 4 Initially factor the numerator and denominator, lim x → 2 x 4 − 1 x 4 − 3 x 2 − 4 = lim x → 2 ( x 2 − 1 ) ( x 2 − 1 ) ( x 2 − 4 ) ( x 2 + 1 ) lim x → 2 x 4 − 1 x 4 − 3 x 2 − 4 = lim x → 2 x 2 − 1 x 2 − 4 , by using direct substitution lim x → 2 x 4 − 1 x 4 − 3 x 2 − 4 = 2 2 − 1 2 2 − 4 lim x → 2 x 4 − 1 x 4 − 3 x 2 − 4 = 3 0 lim x → 2 x 4 − 1 x 4 − 3 x 2 − 4 = undefined Thus we can approximate the limit algebraically.

3rd Edition

ISBN: 9781285607160

Author: Larson

Publisher: CENGAGE CO

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Question

Chapter 12.2, Problem 34E

To determine

To find: To approximate the limit by using a graphing utility to graph the function.

Expert Solution

Answer to Problem 34E

The approximate limit by using a graphing utility to graph the given function does not exist.

Explanation of Solution

Given: $limx→2x4−1x4−3x2−4$

EBK PRECALCULUS W/LIMITS, Chapter 12.2, Problem 34E

The above graph is the graphical representation of the given function with the limits $limx→2x4−1x4−3x2−4$ . From the graph we observe the limit does not exist.

Thus we can find the limit using graphing utility.

To determine

To find: To numerically approximate the limit by using the table feature of the graphing utility to create a table.

Expert Solution

Answer to Problem 34E

The numerically approximate limit using a table from the graph does not exist.

Explanation of Solution

Given: $limx→2x4−1x4−3x2−4$

From the graph we can create a table,

x	f(x)
1.9	-6.692
1.99	-74.188
1.999	-749.188
2	Error
2.001	750.813
2.01	75.813
2.1	8.317

Therefore we can conclude that numerically the limit of the given function does not exist.

To determine

To find: To algebraically evaluate the limit by using the appropriate techniques.

Expert Solution

Answer to Problem 34E

By evaluating the given limit algebraically the limit does not exist.

Explanation of Solution

Given: $limx→2x4−1x4−3x2−4$

Initially factor the numerator and denominator,

$limx→2x4−1x4−3x2−4=limx→2(x2−1)(x2−1)(x2−4)(x2+1)limx→2x4−1x4−3x2−4=limx→2x2−1x2−4, by using direct substitutionlimx→2x4−1x4−3x2−4=22−122−4limx→2x4−1x4−3x2−4=30limx→2x4−1x4−3x2−4=undefined$

Thus we can approximate the limit algebraically.

Chapter 12.2, Problem 33E

Chapter 12.2, Problem 35E

Chapter 12 Solutions

EBK PRECALCULUS W/LIMITS

Ch. 12.1 - Prob. 1E Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E Ch. 12.1 - Prob. 4E Ch. 12.1 - Prob. 5E Ch. 12.1 - Prob. 6E Ch. 12.1 - Prob. 7E Ch. 12.1 - Prob. 8E Ch. 12.1 - Prob. 9E Ch. 12.1 - Prob. 10E

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