2B_midterm2_sample1 - 1 Let f x x x 2 e x a(3 points Find...

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1. Let f ( x ) x x 2 e x . a) (3 points) Find f (0) . b) (2 points) Find f 1 (1) . c) (10 points) Find f 1 (1) . 2. (10 points) Find the average value of f ( x ) e sin 1 x 1 x 2 over the interval 0, 2 2 .
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3. (10 points each) Find dy dx . No need to simplify final answers. a) y cos 1 x sec 1 x b) y x log 3 x 4. (10 points each) Integrate. a) dx x 1 ln x 2
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b) x sec 2 x dx c) e 2 x dx 1 e 4 x
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5. (10 points each) Calculate the following limits.
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