quiz2Bsol - Solutions to Quiz 2B www.math.ufl.edu/...

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Unformatted text preview: Solutions to Quiz 2B 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 cos x = cot x. cos x sin x sin x cos x = cos x sin x cos x − cos x = 0 cos x(sin x − 1) = 0 cos x = Thus, we have either cos x = 0 or sin x = 1. π (a) When cos x = 0, we have x = π , 32 in our interval. 2 (b) When sin x = 1, we have x = π 2 in our interval. π Hence, our solution set is π , 32 . (Did you remember to check to make 2 sure we did not divide by zero?) 3. Determine the validity of the statement. √ (a) ”The domain of x + 5 is [−5, ∞).” This statement is TRUE. 1 (b) ”The graph of f (x) + 3 is obtained by shifting f (x) three units to the left.” This statement is FALSE. The correct statemtent should read: ”The graph of f (x) + 3 is obtained by shifting f (x) three units upward.” 2 ...
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quiz2Bsol - Solutions to Quiz 2B www.math.ufl.edu/...

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