   Chapter 10.3, Problem 113E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

What is wrong with the following statement? If f ( x ) isspecified algebraically and f ( a ) is defined, then lim x → a f ( x ) existsand equals f ( a ) . How can it be corrected?

To determine

Whether the statement “if f(x) is specified algebraically and f(a) is defined, then limxaf(x) exists and is equal to f(a) ” is correct or not.

Explanation

Consider the statement f(x) is specified algebraically and f(a) is defined, then limxaf(x) exists and is equal to f(a).

This statement may be true if the function f(x) is a closed-form function. For the non-closed form function, it may not be true.

For example:

Consider the function f(x)={x   if x20   if x>2.

Here, the function is not in closed-form. It breaks at x=2.

Now, at x=2 the function is x which comes out to be 2. So, the function is defined

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