BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter A, Problem 44E
To determine

To calculate: To show that if 0<a<b , then a2<b2

Expert Solution

Answer to Problem 44E

Its proved that if 0<a<b , then a2<b2

Explanation of Solution

Given information: 0<a<b

Formula Used:

If a and b are real numbers, where c is non-zero real number, then the inequality a<b is same as

  a+c<b+c

  ac<bc   if c>0

  ac>bc   if c<0

Calculation:

Given the following:

  0<a<b

On simplifying,

  a<bab<0

Since a>0,b>0 , thus a+b>0

Multiplying both sides of equation by (a+b) :

  (ab)(a+b)<0(a+b)(ab)(a+b)<0a2b2<0a2<b2

Conclusion:

Hence, proved that a2<b2

Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!