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# handout_10_22 - Does linear approximation say anything...

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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

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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 . .............
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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...
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handout_10_22 - Does linear approximation say anything...

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