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Unformatted text preview: Math 2250 Exam #1 Solutions 1. What is the average rate of change of the function v ( t ) = csc( t ) over the interval [ π/ 6 ,π/ 2]? Answer: The average rate of change of v ( t ) over [ π/ 6 ,π/ 2] is simply v ( π/ 2) v ( π/ 6) π/ 2 π/ 6 = csc( π/ 2) csc( π/ 6) π/ 3 = 1 sin( π/ 2) 1 sin( π/ 6) π/ 3 = 1 1 1 1 / 2 π/ 3 = 1 2 π/ 3 = 1 π/ 3 = 3 π . 2. Determine either of the horizontal asymptotes to the curve y = 3 x 5 2 √ 4 x 2 + 6 x 9 . Answer: Let f ( x ) = 3 x 5 2 √ 4 x 2 +6 x 9 . The curve has a horizontal asymptote y = L if lim x → + ∞ f ( x ) = L or lim x →∞ f ( x ) = L . So that we don’t have to worry about minus signs, let’s evaluate the limit as x goes to + ∞ . To do so, we will multiply by 1 /x 1 /x (since the highest power of x is x 2 , but it’s under a square root so it only counts as degree 1): lim x → + ∞ 3 x 5 2 √ 4 x 2 + 6 x 9 = lim x → + ∞ 3 x 5 2 √ 4 x 2 + 6 x 9 1 /x 1 /x = lim x → + ∞ 1 x ( 3 x 5 2...
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 Fall '08
 CHESTKOFSKY
 Calculus, Derivative, Rate Of Change, lim, Limit of a function, lim g

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