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 9P
To determine

The value of the sum of the constants a+b+c+d in the equation.

Expert Solution

Explanation of Solution

Given information:

The equation is,

  limx0ax2+sinbx+sincx+sindx3x2+5x4+7x6=8

Calculations:

Here the equation is,

  limx0ax2+sinbx+sincx+sindx3x2+5x4+7x6=8

Now the left side of the equation is of the form 00 , therefore we can apply L’Hospotal’s rule.

Thus.

  limx0ax2+sinbx+sincx+sindx3x2+5x4+7x6limx02ax+bcosbx+ccoscx+dcosdx6x+20x3+42x5............(1)

Again the equation is of the form 00 , therefore we can apply L’Hospotal’s rule,

Thus.

  limx02ax+bcosbx+ccoscx+dcosdx6x+20x3+42x5limx02ab2sinbxc2sincxd2sindx6+60x2+210x4limx02a6limx0a3

Now,

  limx0a3=8a=8×3=24

Now the denominator of the equation is zero since x0 . But the limits exists in the equation. So by equating the numerator equal to zero, we get.

, 0+b+c+d=0or,b+c+d=0

Thus the value of a+b+c+d=24.

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!