Chapter 1. RogaCalcET2 2.4.023.Tutorial.SA.

1.1 Problem Statement

eval rand(5,9);
$a-1;

Determine the points of discontinuity. State the type of discontinuity (removable, jump, infinite, or none of these) and whether the function is left- or right-continuous.

1.2 Step 1

Question 1.1

The given function is a XM710SMi641HyNNecqNOfH4LMtA/+uB6FTuzbFDMCSM8K2RI8zMhAA== function and it is continuous 9bNSmg8XLMp82FekXNTzdLcSKM+x6IoldhY6JiT8HszcnOkA4iQuFBtCPKHBFq/uOgkAB4M8XzAUZmbdlvnVsxzdlDKHFILz+T6efMzs2G8=.

Correct.
Incorrect.

1.3 Step 2

Question Sequence

Recall that the domain of a rational function is defined for all values of x except those values for which .

Question 1.2

Solve for x.

x = ftB1gIsQOozdRQwA/JPVx0k4/R6UPT/F9dFxb7cMfFM=.

Correct.
Incorrect.

Question 1.3

Therefore the domain of is all real numbers except

x =ftB1gIsQOozdRQwA/JPVx0k4/R6UPT/F9dFxb7cMfFM=.

Correct.
Incorrect.

Question 1.4

Because it is a rational function, is continuous over it's domain. Thus, is discontinuous at the point x = ftB1gIsQOozdRQwA/JPVx0k4/R6UPT/F9dFxb7cMfFM= since this is the value at which f(x) is not defined.

Correct.
Incorrect.

1.4 Step 3

Recall the possible types of discontinuities.

Question Sequence

Question 1.5

If exists but is not equal to , then x = c is a(n) eHjzXf7gcKm0dLL/5oRTaC348tLf+XHS8ZQobsmQTS4= discontinuity.

Correct.
Incorrect.

Question 1.6

If and exist but are not equal, then x = c is a(n) Au6BjwX198+Y0xRTH+8NaWPj32E2K1ICN2kVgw== discontinuity.

Correct.
Incorrect.

Question 1.7

If one or both of and is infinite, then x = c is a(n) 8Zch0aesnQY3cV5BJQoTpBdBoGzhcVMmL27UzU0slrA= discontinuity even if itself is not defined at x = c.

Correct.
Incorrect.

Question 1.8

To determine the type of discontinuity at , find the one-sided limits as x approaches .

=ugHNTI1hRxM=

=3LecBr2w/JA=

(Use "inf" for ∞ and "-inf" for -∞)

Correct.
Incorrect.

Question 1.9

zt6or9YIfJ0+1XnN22SK5a4Bvmr1QEf/bMLiKqB+V1gqZOdkTuc/VYZzsQVqlAKRBwQqVDfGgDaAtUPQbmmkRMxlPcbBKFgYJYHcOiwDA1dnmqfs0C32JRgJxw4rgQCAYbY5q2Wa15TpvQAA1MB+e86GoggfBvghhR+T9UaQkSJtKHH+Rrma3mWT0Z2pftWkDLV1c1BlRLK04E8dIua/3nFPilWYypxuY6IlEz6Su8t4AflITSkuo1CUorDlv5tywjkSLVxqzd5jR6/Dm04xBg2absrDdcmCRrIi0HFfeHuXk2M2yHDNKBYDh5MjbsZrWmMuzry+M+E=
Correct.
Incorrect.

1.5 Step 4

Recall the definition of a one-sided continuity at x = c for a given function .

Question 1.10

If , the function is T1QAvMquxITmteCofDF98w==-continuous at x = c.

If , the function is y/8elwqLKvMQPfWtffwxDQ==-continuous at x = c.

Correct.
Incorrect.

Question 1.11

A graph of the function is shown below (c = $b/$a).

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
Correct.
Incorrect.
true