Chapter 14: Q. 41 (page 876)

In Problem, graph each function. Use the graph to find the indicated limit, if it exists.
$\underset{x \to 0}{l i m} f (x), f (x) = \{\begin{cases} \sin (x) & i f x \leq 0 \\ x^{2} & i f x > 0 \end{cases}$

Short Answer

Expert verified

The value of given function (at x= 0 ) is : 0

Step by step solution

Step1. Given information

The given function $\underset{x \to 0}{l i m} f (x), f (x) = \{\begin{cases} \sin (x) & i f x \leq 0 \\ x^{2} & i f x > 0 \end{cases}$

Step2. checking the existence of the limit at a given point

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 0

Thus the limit of the given function is evaluated by 0

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In Problem, graph each function. Use the graph to find the indicated limit, if it exists.
$\underset{x \to 0}{l i m} f (x), f (x) = \{\begin{cases} \sin (x) & i f x \leq 0 \\ x^{2} & i f x > 0 \end{cases}$

Short Answer

Step by step solution

Step1. Given information

Step2. checking the existence of the limit at a given point

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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)=sinxifx≤0x2ifx>0

Short Answer

Step by step solution

Step1. Given information

Step2. checking the existence of the limit at a given point

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Theoretical and Mathematical Physics

Statistics

Pure Maths

Logic and Functions

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In Problem, graph each function. Use the graph to find the indicated limit, if it exists.
$\underset{x \to 0}{l i m} f (x), f (x) = \{\begin{cases} \sin (x) & i f x \leq 0 \\ x^{2} & i f x > 0 \end{cases}$