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handout_10_14 - a Show that y t = sin t and y t =-cos t...

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Math 1a: Derivatives of trigonometric functions October 14, 2009 1. Use d dx sin x = cos x and d dx cos x = - sin x to compute a. d dx tan x b. d dx cot x c. d dx sec x d. d dx csc x 2. Find the following limits. a. lim h 0 tan h h b. lim h 0 sin 2 h sin h 3. Determine the following derivatives. a. d du (sin 2 u + 3 cos u ) b. d dx x 2 sin x c. d dx sin( x ) + cos( x ) sin( x ) 1
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4. Bob decides to go bungee jumping. He attaches an elastic cord to his feet and jumps off a very tall bridge. At time t = 0, he reaches the bottom of his descent and starts to oscillate. At time t , his acceleration is given by y 00 ( t ) = - y ( t ) , where y ( t ) is his height (relative to some convenient reference point).
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Unformatted text preview: a. Show that y ( t ) = sin( t ) and y ( t ) =-cos( t ) both satisfy the given differential equation. b. Can you find some other functions that also satisfy the differential equation? c. In reality, Bob’s oscillatory motion will slowly fade away. A more realistic differential equation would be y 00 ( t ) =-2 y ( t )-2 y ( t ) . Check that y ( t ) = e-t sin( t ) satisfies this equation. 2...
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