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StudyGuideTest1

# StudyGuideTest1 - Study Sheet for Test 1 Honors Calculus...

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Study Sheet for Test 1 Honors Calculus Keesling Test on 9/14/07 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. 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. At the points of discontinuity determine whether the function has a removable discontinuity or vertical asymptote. f ( x ) = x + 2 x 2 ! 3 x ! 10 6. Let p ( x ) = x 3 ! 2 x + 5 . Show that p ( x ) has a zero in the interval [ ! 3, ! 2] . Find an approximation to this zero with four digits accuracy. 7. Show that p ( x ) = x 9 + 2 x 2 ! 5 x + 1 has at least three distinct real zeros. Find approximations to each of these roots using the bisection method.

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StudyGuideTest1 - Study Sheet for Test 1 Honors Calculus...

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