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Q. 90

Found in: Page 122


Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

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Short Answer

Write a delta–epsilon proof that proves that f is continuous on its domain. In each case, you will need to assume that δ is less than or equal to 1.


Ans: x3 is continuous in its domain xR

See the step by step solution

Step by Step Solution

Step 1. Given information.

given expression f(x)=x3

Step 2. Domain: 

Since, x is defined fo all xR

Step 3. So, check for continuity. 

Let c be any real number.

f is continuous at x=c

assume that c is less than or equal to 1

if, limxcf(x)=f(c)


by putting x=c

localid="1648044466347" =c3

RHS = f(c)=c3

Step 4. Since, LHS=RHS

So, Function is continuous at x=c

Thus, we can write that

f(x)=x3 continuous for all xR

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