Q. 75 Describe the intervals on which ... [FREE SOLUTION]

Chapter 1: Q. 75 (page 136)

Describe the intervals on which each function f is continuous. At each point where f fails to be
continuous, use limits to determine the type of discontinuity
and any left- or right-continuity.

Short Answer

Expert verified

The interval on which the function is discontinuous

Step by step solution

Step 1. Given information

The given information is $f (x) = \{\begin{cases} \frac{x^{2} - 1}{x - 1}, i f x < 1 \\ 0, i f x = 1 \\ 3 x - 1, i f x > 1 \end{cases}$

Step 2. Calculate the left and right limits

$\lim_{x 鈫� 1^{-}} f (x) = \lim_{x 鈫� 1^{-}} (\frac{x^{2} - 1}{x - 1}) = (\frac{(1^{2} - 1)}{1 - 1}) = 0$

$\lim_{x 鈫� 1} f (x) = \lim_{x 鈫� 1} (0) = 0$

$\lim_{x 鈫� 1^{+}} f (x) = \lim_{x 鈫� 1^{+}} (3 x - 1) = (3 (1) - 1) = 2$

since the left and right limits both exists but not equal

hence it is discontinuous

Step 3. The solution

Hence the function is discontinuous

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Describe the intervals on which each function f is continuous. At each point where f fails to be
continuous, use limits to determine the type of discontinuity
and any left- or right-continuity.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculate the left and right limits

Step 3. The solution

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91影视

Describe the intervals on which each function f is continuous. At each point where f fails to becontinuous, use limits to determine the type of discontinuityand any left- or right-continuity.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculate the left and right limits

Step 3. The solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Logic and Functions

Decision Maths

Probability and Statistics

Applied Mathematics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Describe the intervals on which each function f is continuous. At each point where f fails to be
continuous, use limits to determine the type of discontinuity
and any left- or right-continuity.