Chapter 14: Q. 42 (page 876)

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

Short Answer

Expert verified

the limit of a given function at x=0 is 0

Step by step solution

step1. Given information

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

step2. Explanation about the existence of a 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

so according to the question, we can see in the pieces of both graphs when x is near 0, then y approach 1 in both pieces of the graph

Thus the limit of the given function is evaluated by 1

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

Short Answer

Step by step solution

step1. Given information

step2. Explanation about the existence of a limit of the given function

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In Problem, graph each function. Use the graph to find the indicated limit, if it exists.limx→0f(x),f(x)=exifx>01-xifx≤0

Short Answer

Step by step solution

step1. Given information

step2. Explanation about the existence of a limit of the given function

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Calculus

Decision Maths

Statistics

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Discrete Mathematics

Study anywhere. Anytime. Across all devices.

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