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# 5th - B is sailing north at 25km/h How fast is the distance...

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Math119 Recitation 5 October 18, 2006 1. Find a formula for f n ( x ) for f ( x ) = (1 + x ) - 1 . 2. Find the given derivative by observing the pattern f 35 ( x ); where f ( x ) = x sin x 3. Find constants A, B, C such that the function y = Ax 2 + Bx + C satisﬁes the diﬀerential equation y 00 + y 0 - 2 y = x 2 4. A plane ﬂying horizontally at an altitude of 1mi and a speed of 500mi/hr passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 2mi away from the station. 5. A man starts walking north at 4ft/s from a point P . Five minutes later a woman starts walking south at 5ft/s from a point 500ft due east of P . At what rate are the people moving apart 15min after the woman starts walking. 6. At noon ship A is 100km. west of ship B . Ship A is sailing south at 35km/h and ship

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Unformatted text preview: B is sailing north at 25km/h. How fast is the distance between the ships changing at 4:00pm., 7. Use linear approximation to estimate the given number: (a) (8 . 06) 2 3 (b) cos 31 . 5 ◦ 8. Use diﬀerentials to estimate the amount of paint needed to apply a coat of paint 0 . 05cm thick to a hemispherical dome with diameter 50m. 9. (a) Sketch the graph of a function on [-1 , 2] that has an absolute maxi-mum but no local maximum. (b) Sketch the graph of a function on [-1 , 2] that has a local maximum but no absolute maximum. 10. Find the absolute maximum and absolute minimum values of f on the given interval 1 (a) f ( x ) = x x 2 +1 on [0 , 2] (b) f ( x ) = sin x + cos x on [0 , π/ 3] 2...
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5th - B is sailing north at 25km/h How fast is the distance...

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