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 4, Problem 45RE
To determine

To find: The minimum velocity of the length of the wave.

Expert Solution

Answer to Problem 45RE

The minimum velocity of the length of the wave is L=C

Explanation of Solution

Given information:

The velocity of a wave of length L in deep water is V=k1C+CL

Calculation:

Consider the velocity of a wave,

  V=k1C+CL=kL2+CCL

Where k and C are the positive constants,

Then derivation of V with respect to L,

  V=k(L2C2)2CL2L2+C2CL

Length L is a positive quantity so L2+CCL0,[c>0]

And V=0 when L2C2=0 or L=C

So V has an absolute minimum at L=C

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!