MATH-137-1039-Midterm1_exam

# MATH-137-1039-Midterm1_exam - 4 Find the domain of the...

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MATH 137 — Fall 2003 — Midterm #1 Page 1 of 1 Reprinted by MathSoc ./ Instructors I. VanderBurgh, F. Zorzitto, J. Koeller, S. Sivaloganathan, P. Wood, D. Park, B. Marshman, C. Colijn, C. Struthers, D. Harmsworth, C. B. Chua Time 90 minutes 1. (a) Evaluate cos 7 π 6 and tan 7 π 6 . Calcuator-based answers are not acceptable. (b) Solve cos x - sin 2 x = 0 for all x in the interval [0 , 2 π ]. 2. Sketch the set of points ( x, y ) in R 2 that satisfy the inequality | x | - | y | ≤ 1. Be sure to show how you get your solution. 3. On coordinate axes, sketch the graph of f ( x ) = x +1 x 2 - 9 , clearly indicating all intercepts and asymptotes. Give reasons for your sketch. There is no need to use derivatives.
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Unformatted text preview: 4. Find the domain of the function ( x ) = ln( x +1)+ln( x-1). Then ﬁnd all x such that ln( x +1)+ln( x-1) ≤ 1. 5. (a) Explain why arcsin x = arctan ± x √ 1-x 2 ² for every x in the interval (-1 , 1). (b) Sketch y = arctan( x-1), clearly indicating all intercepts and asymptotes. 6. Let f ( x ) = ³ 1 + x when x < e x when x ≥ (a) Sketch the graph of f and also the graph of its inverse function f-1 oncoordinateaxes± (b) Use the graph of the function f-1 that you obtained above to write a formula for f-1 ( x )....
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