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 . Di±erentiating, 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...
View
Full Document
 Winter '07
 JonathanRogawski
 Pythagorean Theorem, UCI race classifications, Tour de Georgia, Solution. Let, JED YANG

Click to edit the document details