handout_11_16 - 5 Find a function f x such that f x = 2 e...

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MATH 1A: ANTIDERIVATIVES 1. Water is leaking out of a tank at the rate of (10 - t ) liters per minute, where t is time in minutes. The leaking starts at t = 0. How much water has leaked after 4 minutes? What if the leak had started at t = 1? 2. For each of the following functions f ( x ), find all functions g ( x ) such that g 0 ( x ) = f ( x ): (1) f ( x ) = cos( x ) + sin( x ) (2) f ( x ) = 3 x - 1 + x 2 (3) f ( x ) = e 2 x - e - 2 x 2 (4) f ( x ) = 3 1+ x 2 3. Alyssa and Ben are both trying to find an antiderivative of - 2 ( x +1) 2 . Alyssa comes up with 1 x +1 and Ben with - x x +1 . Who is correct? Date : November 16, 2009. 1
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4. Find a function whose derivative is 1 /x 3 and which has the line y = 1 as a horizontal asymptote.
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Unformatted text preview: 5. Find a function f ( x ) such that f ( x ) = 2 e x-5 x and f (0) = 0. How many such functions are there? 6. A mass oscillates on a spring. Initially, it is released from rest and the length of the spring is 5cm. After t seconds, the acceleration of the mass is-2 cos( t ) What is the length of the spring after t seconds? 7. Find all continuous function g ( x ) whose derivative g ( x ) satisfies g ( x ) = (-1 if x < 1 if x > . Can such a function be differentiable at 0? 2...
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