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P MT 12

# P MT 12 - lim x → 1 x 3-1 x 2-1 1 5 Let f x = 3 1/x In...

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Math 1A Calculus Fall, 2004 Prof. Haiman First Midterm Exam Name Student ID Number Section You may use one sheet of notes. No other notes, books or calculators. There are 9 questions, on front and back. Each question is worth 11 points. You get 1 point for free. Write answers on the exam and turn in only this paper. Show work or brieﬂy indicate a reason for your answers. 1. Find the domain of the function f ( x ) = x - 3 - x . 2. Find a formula for the inverse function g ( x ) of the function f ( x ) = e x 2 +1 . 3. Evaluate the limit, if it exists (possibly as an inﬁnite limit). lim x 3 - x - 5 x - 3 . 4. Evaluate the limit, if it exists (possibly as an inﬁnite limit).

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Unformatted text preview: lim x → 1 x 3-1 x 2-1 . 1 5. Let f ( x ) = 3 + 1 /x . In the deﬁnition of the limit lim x →∞ f ( x ) = 3, if ε = 1 / 5, how large must N be to guarantee that | f ( x )-3 | < ε for all x > N ? 6. Show that the equation x 4-x-1 = 0 has at least one real solution in the interval (1 , 2). 7. Diﬀerentiate the function f ( x ) = 2 x + 1 x + 3 . 8. Diﬀerentiate the function f ( x ) = √ x e x . 9. Find the values of x where the graph of y = x 3-6 x 2 has a horizontal tangent line. 2...
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P MT 12 - lim x → 1 x 3-1 x 2-1 1 5 Let f x = 3 1/x In...

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