StudyGuideTest1(2008)

StudyGuideTest1(2008) - Study Sheet for Test 1 Honors...

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Study Sheet for Test 1 Honors Calculus Keesling Test on 9/24/08 1. Compute the following limits. (a) lim x ! 2 x 3 " 2 x ( ) (b) lim x ! 0 x " sin 1 x ( ) (c) lim x ! 1 x 3 " 1 x 2 " 1 (d) lim x ! 0 x + 1 " 1 x (e) lim x ! 0 tan( x ) sin( x ) (d) lim x ! 0 x " cos 1 x 2 ( ) 2. Determine which numbers are represented by the following decimal expansions (a) .99 9 (b) 203.71914 (c) ! 1.2031 3. Define a rational number. Give an argument that the following decimal expansion cannot represent a rational number .1010010001 ! 100 ! 0 n zeros "#$ 1 ! . 4. Prove that the following limit holds for any x < 1 x n n = 0 ! " = 1 1 # x . Also, be able to use this formula: (a) 1 3 ( ) n n = 0 ! " (b) ! 1 9 ( ) n n = 1 " # (c) 1 3 ( ) n n = 2 ! " (d) 3 n n = 0 3000 ! 5. Newton used the tangent line to approximate a zero of a function f . He did this by taking a value where f is near zero, say x 0 . The point x 0 is the first approximation of a zero of f . He then considered where the tangent line through the point ( x 0 , f ( x 0 )) crossed the x –axis. Call this point x 1 . This should be a better approximation the zero of f than x 0 . The process continues. Demonstrate the formula for x n + 1 in terms of x n given below.
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StudyGuideTest1(2008) - Study Sheet for Test 1 Honors...

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