handout_10_22 - Does linear approximation say anything...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 1a: Linear approximation October 22, 2009 1. Use linear approximation to estimate the following without your calculator. Write down the linear function that you used for your approximation and the approximate value you obtained. 1. 3 1006 2. sin( - 0 . 01) 3. log(1 . 02) 4. cos(0 . 01) 5. 1 998 6. (1 . 001) 100 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2. When blood flows along a blood vessel, the flux F (the volume of blood per unit time that flows past a given point) is proportional to the fourth power of the radius R of the blood vessel: F = kR 4 . Show that the relative change in F is about four times the relative change in R . Complete the following sentence: If the radius decreases by 2% then the flux would decrease (approximately) by . .............
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: %. Does linear approximation say anything meaningful about the change in flux when the radius changes from 1mm to 3mm? 3. A pendulum is swinging from side to side. At time t , the angle between the pendulum and a vertical line is θ ( t ). It is known that θ ( t ) satisfies the differential equation θ 00 ( t ) =-sin( θ ( t )) . 1. This equation is too hard to solve. Use linearization to approximate the right hand side when θ ( t ) is very small. 2. Replace the right hand side with the linear approximation you found. Show that θ ( t ) = C cos( t ) is a solution to the new differential equation, where C is a constant. 2...
View Full Document

Page1 / 2

handout_10_22 - Does linear approximation say anything...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online