Q. 74 Describe the intervals on which ... [FREE SOLUTION]

Chapter 1: Q. 74 (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.
$f (x) = \{\begin{cases} \frac{3 x^{2}}{4 + x}, i f x < 2 \\ x^{2} - 2, i f x 鈮� 2 \end{cases}$

Short Answer

Expert verified

The interval on which the function is continuous is 2

Step by step solution

Step 1. Given information

The given information is $f (x) = \{\begin{cases} \frac{3 x^{2}}{4 + x}, i f x < 2 \\ x^{2} - 2, i f x 鈮� 2 \end{cases}$

Step 2. Calculate the left and right limits

$\lim_{x 鈫� 2^{-}} f (x) = \lim_{x 鈫� 2^{-}} (\frac{3 x^{2}}{4 + x}) = (\frac{3 {(2)}^{2}}{4 + 2}) = \frac{12}{6} = 2$

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

since the left and right limits both exists and are equal to 2

therefore f is continuous at 2

Step 3. The solution

The interval on which function is continuous is 2

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91影视

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.
$f (x) = \{\begin{cases} \frac{3 x^{2}}{4 + x}, i f x < 2 \\ x^{2} - 2, i f x 鈮� 2 \end{cases}$

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.fx=3x24+x,ifx<2x2-2,ifx鈮�2

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

Discrete Mathematics

Mechanics Maths

Probability and Statistics

Decision Maths

Logic and Functions

Statistics

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.
$f (x) = \{\begin{cases} \frac{3 x^{2}}{4 + x}, i f x < 2 \\ x^{2} - 2, i f x 鈮� 2 \end{cases}$