Use differentials to approximate the arc length of the graph of the equation from P to Q. Round answer to four decimal places. $y=x^{2}+3$ P (3, 12), Q (3.2, 13.24)
A) 6.0828
B) 3.6497
C) 1.2166
D) 2.4331

Question

Quizplus · Accepted Answer

To approximate the arc length, use the formula $ ds = \sqrt{1 + (dy/dx)^2} \, dx $. The derivative $ dy/dx = 2x $. At $ x = 3 $, $ dy/dx = 6 $. So, $ ds \approx \sqrt{1 + 6^2} \, dx = \sqrt{37} \, dx $. The change in $ x $ is $ 0.2 $. Thus, the approximate arc length is $ \sqrt{37} \times 0.2 \approx 1.2166 $.

Use Differentials to Approximate the Arc Length of the Graph y=x2+3y=x^{2}+3y=x2+3

Use Differentials to Approximate the Arc Length of the Graph $y=x^{2}+3$