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Chapter 2: Q. 20 (page 184)

Express the following limit statement as delta鈥揺psilon statement:

f'(3)=limx鈫�3鈥�x2鈭�9x鈭�3

Short Answer

Expert verified

lim螖x鈫�0鈥�螖y螖x

Step by step solution

01

Step 1. Given information

We have been given a limit statement as:

f'(3)=limx鈫�3鈥�x2鈭�9x鈭�3

We have to express it as delta鈥揺psilon statement.

02

Step 2. Express the limit as a delta-epsilon statement

Let,

x1=3x2=xy1=9y2=x2

So,

螖x=x2鈭�x1=x鈭�3螖y=y2鈭�y1=x2鈭�9

When x鈫�3then x-3鈫�0or 鈭�x鈫�0

Therefore, replace the values with the delta notations as follows:

f鈥�(3)=limx鈫�3鈥�x2鈭�9x鈭�3=lim螖x鈫�0鈥�螖y螖x

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