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Unformatted text preview: I run 60 2 + x 2 on grass, and then run on sidewalk for 300x . Dividing by the rates, we get the total travel time is y = 300 x 13 + 60 2 + x 2 5 . Dierentiating, we get y =1 13 + x 5 60 2 + x 2 . Setting equal to 0, we solve and get x = 25. Note that if there were a sidewalk on the short side too, then it would be faster to skate along the sidewalk for the entire time instead. Moral: Sometimes it is not good to cut corners. s 2. Basic Integration 2.1. Exercise 4.8.58. Let f ( t ) = tcos t , f (0) = 2, f (0) =2. Find f and f . Solution. By integrating, we see f ( t ) = t 2 / 2sin t + c . Since f (0) = c = 2, we get f ( t ) = t 2 / 2sin t + 2. Integrating again to get f ( t ) = t 3 / 6 + cos t + 2 t + d . Since f (0) = 1 + d =2, we get d =3, yielding f ( t ) = t 3 /y + cos t + 2 t3. s...
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This note was uploaded on 09/19/2011 for the course MATH 31A taught by Professor Jonathanrogawski during the Winter '07 term at UCLA.
 Winter '07
 JonathanRogawski
 Pythagorean Theorem

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