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assignment3 - ma2176 a3 1 Applications of Derivatives An...

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1 ma2176 a3 Applications of Derivatives 1. An airplane, flying horizontally at an altitude of 1 km, passes directly over an observer. If the constant speed of the plane is 240 km per hour, how fast is its distance from the observer increasing 30 seconds later? 2. Water is pumped at a uniform rate of 2 liters per minute into a tank shaped like a frustum of a right circular cone. The tank has altitude 80 centimeters, and its lower and upper radii are 20 and 40 centimeters respectively. How fast is the water level rising when the depth of the water is 30 centimeters? (Hint: The volume V of a frustum with altitude l and lower and upper radii a and b is ( ) 2 2 1 3 V l a ab b π = + + ) 3. A particle P is moving along the graph of 2 , 4 2 = x x y , so that the x- coordinate of P is increasing at the rate of 5 units per second. How fast is the y- coordinate of P increasing when 3 = x ? 4. Let 1 ) ( 2 3 2 + = = x x x f y . (a) Evaluate ( ) ' f x for 0 x and prove that ( ) ' 0 f does not exist.
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