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P MT 14 w sln

# P MT 14 w sln - Math 1A Midterm 1 11:00-12:30pm You are...

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Math 1A Midterm 1 2005-9-29 11:00-12:30pm. You are allowed 1 sheet of notes. Calculators are not allowed. Each question is worth 3 marks, which will only be given for a clear and correct answer. 1. Find the domain of the function g ( u ) = u + 2 - u . 2. Sketch the graph of y = | x 2 - 2 x | . 3. Find a formula for the inverse of the function f ( x ) = 1 + e x 3 . 4. Sketch the graph of a function f that satisfies the conditions lim x 0 - f ( x ) = 1 , lim x 0 + f ( x ) = - 1 , lim x 1 - f ( x ) = 1 , lim x 1 + f ( x ) = - 1 , f (2) = 1 . 5. Evaluate the limit lim x 1 x 3 - 1 x 2 - 1 6. How close to 2 do we have to take x so that 5 x + 3 is within a distance of 0.01 from 13? 7. Find the numbers at which f is discontinuous, where f is defined by f ( x ) = x 2 if x 1, f ( x ) = 1 /x if 1 < x < 3, f ( x ) = 1 / 2 + x - 3 if x 3. 8. What is lim x →-∞ (3 x + 1)(4 x + 1) ( x + 1)(2 x + 1) 9. A curve has equation y = f ( x ). Write an expression for the slope of the secant line
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