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Chapter 6: Q. 23 (page 539)

Approximate the arc length of f (x) on [a, b], using n line segments and the distance formula. Include a sketch of f (x) and the line segments .

fx=9-x2,a,b=-3,3,n=3

Short Answer

Expert verified

The arc length is 13.996.

The graph is as below:

Step by step solution

01

Step 1. Given information .

Consider the given functionfx=9-x2.

02

Step 2. Formula used .

Arc length=limn鈫�鈭�鈭�k=1n1+鈭�yk鈭�x2路鈭�x

03

Step 3. Find the arc length .

fx=9-x2,a=-3,b=3,n=3鈭�x=b-an=3+33=2xk=a+k鈭�xx0=-3+0=-3,x1=-3+1脳2=-1x2=-3+2脳2=1,x3=-3+3脳2=3鈭�y1=fx1-fx0=8-0=8=2路828鈭�y2=fx2-fx1=8-8=0鈭�y3=fx3-fx2=0-8=-2.828Arclength=1+2.82822+1+0+1+-2.82822脳2=21+1.4142+1脳2=2脳2.999+1脳2=13.996

04

Step 4. Sketch of the function fx=9-x2.

The sketch of the given function is shown below .

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