Chapter 14: Q. 37 (page 876)

In Problem, graph each function. Use the graph to find the indicated limit, if it exists
$\underset{x \to 1}{l i m} f (x), f (x) = \{\begin{cases} 3 x & i f x \leq 0 \\ x + 1 & i f x > 0 \end{cases}$

Short Answer

Expert verified

limit of the function at x=1 doesn't exist

Step by step solution

Step1. Given information

The given function $\underset{x \to 1}{l i m} f (x), f (x) = \{\begin{cases} 3 x & i f x \leq 0 \\ x + 1 & i f x > 0 \end{cases}$

Step2. Calculations of the limit of the given function

To find the limit we have to draw the graph of its

We know that at the limit point as x-factor is near to limit points so that time y tends to a specific value, that specific value is the value of the function at the limit point

According to the question when x is near 1

the first segment of the graph is near 3 but the second segment tends to be 2

The value of both parts of the graph is different at the same value, so on this value limit of given function doesn't exist

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In Problem, graph each function. Use the graph to find the indicated limit, if it exists
$\underset{x \to 1}{l i m} f (x), f (x) = \{\begin{cases} 3 x & i f x \leq 0 \\ x + 1 & i f x > 0 \end{cases}$

Short Answer

Step by step solution

Step1. Given information

Step2. Calculations of the limit of the given function

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In Problem, graph each function. Use the graph to find the indicated limit, if it existslimx→1f(x),f(x)=3xifx≤0x+1ifx>0

Short Answer

Step by step solution

Step1. Given information

Step2. Calculations of the limit of the given function

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Statistics

Theoretical and Mathematical Physics

Probability and Statistics

Applied Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

In Problem, graph each function. Use the graph to find the indicated limit, if it exists
$\underset{x \to 1}{l i m} f (x), f (x) = \{\begin{cases} 3 x & i f x \leq 0 \\ x + 1 & i f x > 0 \end{cases}$