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Chapter 2: Q. 19 (page 184)

Express each of the following limit statements as delta鈥揺psilon statements:

f'3=limh鈫�03+h2-9h

Short Answer

Expert verified

lim鈭�x鈫�0鈭�y鈭�x

Step by step solution

01

Step 1. Given information

We have been given a limit statement as:

f'3=limh鈫�03+h2-9h

We have to express it as delta鈥揺psilon statement.

02

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

Let,

x1=0x2=hy1=9y2=3+h2

So,

鈭�x=x2-x1=h-0=h鈭�y=y2-y1=3+h2-9

When h鈫�0then 鈭�x鈫�0

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

f'3=limh鈫�03+h2-9h=lim鈭�x鈫�0鈭�y鈭�x

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