StudySheetTest1_09

StudySheetTest1_09 - Study Sheet for Test 1 MAC 3472,...

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Unformatted text preview: Study Sheet for Test 1 MAC 3472, Honors Calculus 1 Keesling Test on 9/23/09 1. Compute the following limits. (a) lim x ! 2 ( x 3 " 2 x ) (b) lim x ! x " sin 1 x ( ) (c) lim x 1 x 3 1 x 4 1 (d) lim x x + 1 1 x (e) lim x tan x sin x (f) lim x ! x " cos 1 x 2 ( ) 2. Determine which numbers are represented by the following decimal expansions. (a) .928 (b) ! 27.623 (c) .7532 3. Define a rational number. Give an example of a number that is not rational based on its decimal expansion. 4. Prove that x n n = ! " = 1 1 # x for any x < 1 . 5. Find the following finite and infinite sums. (a) 1 4 ( ) n n = ! " (b) 1 3 ( ) n n = 1 ! " (c) 4 n n = 2 50 ! (d) ! 2 3 ( ) n n = " # 6. Newton used the tangent line to approximate a zero of a function f . Let x be a point near where f is zero and let x 1 be determined by where the tangent line at the point x , f ( x ) ( ) on the graph of f crosses the x axis. Show that x 1 = x !...
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StudySheetTest1_09 - Study Sheet for Test 1 MAC 3472,...

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