quiz2Asol - Solutions to Quiz 2A www.math.ufl.edu harringt...

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Unformatted text preview: Solutions to Quiz 2A www.math.ufl.edu/ harringt January 17, 2008 1 1. Let f (x) = x . Find f (x)−f (b) . x− b Be sure to SIMPLIFY. −1 b x−b b−x = xb(x − b) x−b =− xb(x − b) 1 =− xb f (x) − f (b) = x−b 1 x 2. Find ALL values of x in the interval [0, 2π ] that satisfy sin x = tan x. sin x cos x cos x sin x = sin x cos x sin x − sin x = 0 sin x(cos x − 1) = 0 sin x = Thus, we have either sin x = 0 or cos x = 1. (a) When sin x = 0, we have x = 0, π, 2π in our interval. (b) When cos x = 1, we have x = 0, 2π in our interval. Hence, our solution set is {0, π, 2π }. (Did you remember to check to make sure we did not divide by zero?) 3. Determine the validity of the statement. 1 √ (a) ”The domain of x + 3 is (−3, ∞).” √ This statement is FALSE. It should read ”The domain of x + 3 √ is [−3, ∞).” Notice that we allow −3 in the domain of x + 3. (b) ”The graph of f (x + 2) is obtained by shifting f (x) two units to the left.” This statement is TRUE. 2 ...
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This note was uploaded on 07/10/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

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quiz2Asol - Solutions to Quiz 2A www.math.ufl.edu harringt...

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