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Chapter 1: Q. 10 (page 135)

Write the product rule for limits in terms of delta鈥揺psilon statements.

Short Answer

Expert verified

Product rule for limits in terms of delta鈥揺psilon statements |f(x)g(x)-LM|<蔚

WhereL=limx鈫�cf(x)andM=limx鈫�cg(x)

Step by step solution

01

Step 1. Given information

Let given limitsf(x)andg(x)

02

Step 2. Write the product rule for limits in terms of delta–epsilon statements. 

The product rule for limit is

limx鈫�c[f(x).g(x)]=limx鈫�cf(x).limx鈫�cg(x)

The strategy is to write the limit expression in delta-epsilon statement

For all 蔚>0,there exists 未>0such that if 0<|x-c|<未

Then,

|(f(x)g(x))-(LM)|<蔚|f(x)g(x)-LM|<蔚WhereL=limx鈫�cf(x)andM=limx鈫�cg(x)

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