# Test1 - x 7 20 = Give the starting point Give the solution...

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1 Name MAC 3472 Honors Calculus I Keesling Test 1 9/23/09 Do all problems. Show your work and explain your answers. Each problem is 20 points. 1. Compute the following. (a) lim x ! 1 x 4 " 3 x 2 + 5 ( ) (b) lim x ! 0 x 2 " sin 1 x 3 ( ) (c) d dx x + 3 sin( x ) ! " # \$ % (d) d dx x 3 ! sin( x ) ! ln( x ) ( ) 2. Show the following. (a) Show that 1 n n = 1 ! " = ! . (b) Show that ( ! 1) n + 1 n n = 1 " # has a finite limit.

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2 3. Use Newton’s Method to solve the equation
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Unformatted text preview: x 7 ! 20 = . Give the starting point. Give the solution to ten decimal places. Give a brief explanation of the method. 4. Prove that the following limit holds for any x < 1 , x n n = ! " = 1 1 # x . 3 5. What is the circular cylinder of largest volume that can be inscribed in a sphere of radius R ?...
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Test1 - x 7 20 = Give the starting point Give the solution...

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