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16A-WQ08

# 16A-WQ08 - Math 16A Short Calculus Final Exam Name...

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Math 16A Short Calculus Final Exam Name: Signature: Directions: Turn off all cell phones now. Do not open your test until directed. You may not use books, notes, calculators, or cell phones on this test. Read each problem carefully. Make sure you answer every part of each problem. You have 2 hours. Show your work! Good luck!

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1. Continuity (60 points) For each of the following functions, state: the range, the inter- val(s) on which the function is continuous, and for each disconti- nuity whether or not the discontinuity is removable. (60 points, 15 points each) (a) y = x 2 + 4 (b) y = x +2 x 2 4 (c) y = 2 x (d) y = 4 cos( θ ) + 1

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2. Slope and Derivative (50 points) (a) Find an equation of the line tangent to f ( x ) = x 2 + 1 with slope 2. (20 points) (b) Use the limit definition to find the derivative of the following functions (30 points; 15 points each) i. f ( x ) = x 2 1 ii. h ( t ) = 2 t
3. Rates of Change (45 points) (a) The profit P from selling x units of a product is given by P = 15 + 12 x 81 x .

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16A-WQ08 - Math 16A Short Calculus Final Exam Name...

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