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math1a - quiz 1 - solns

math1a - quiz 1 - solns - Math 1A Quiz 1 Solutions February...

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Math 1A Quiz 1 Solutions February 2nd, 2008 Let f ( x ) be the function: f ( x ) = sin x , x < π 2 3 , x = π 2 x - π 2 + 1 , x > π 2 a) Graph this function. Solution: I don’t have the tech knowledge to make this graphic, but the description in words is as follows: to the left of the line x = π 2 , the graph is the graph of sin( x ); if you don’t recall what this looks like, go look it up on Wikipedia. At the point ( π 2 , 1), there’s an open circle (indicating that this point is not part of our graph, but that the points of sin( x ) approach this point). There’s a single point at ( π 2 , 3). To the right of the line x = π 2 , we have a line with slope 1 emanating from the open circle at ( π 2 , 1) (this is the line y = x - π 2 + 1). Note: If you can’t follow any of the above, please see me at office hours and I’ll be happy to draw this graph for you. b) Does lim x π 2 f ( x ) exist? If so, what is the value of this limit? If not, explain why not. (You don’t need to prove it!) Solution: The limit exists, and is equal to 1. To check that the limit exists,
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