quizsoln10 - Name Math 155 November 2006 Instructions This...

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Name:___________________________ Math 155 Quiz 11 14 November 2006 Instructions : This quiz is closed book and closed notes. You may use a calculator. Label your answers and show all work. SHOW ALL WORK! 1. Give the function f ( x ) = 2 x 3 2 a) Find the equation for the tangent of the function at the point x 0 = 4 . f '( x ) = 3 x 1 2 f (4) = 2(8) =16 f '(4) = 3(2) = 6 f ^ 4 ( x ) = 6( x - 4) +16 or f ^ 4 ( x ) = 6 x - 8 b) Use the tangent line to approximate 2 5 3 f ^ 4 (5) = 6 +16 = 22 or f ^ 4 (5) = 30 - 8 = 22 2. Given the discrete-time dynamical system x t +1 = cos( x t ) + 2 a) Give a function f ( x ) in the form necessary to use Newton’s Method to find equilibria.
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Unformatted text preview: 0 = cos( x *) + 2 -x * so f ( x ) = cos( x ) + 2 -x b) Find the derivative of f ( x ) . f '( x ) = - sin( x ) - 1 c) Write the discrete-time dynamical system representing Newton’s Method for this particular example. (Hint: You should use part (a) and (b)) x t +1 = x t-cos( x ) + 2 -x- sin( x ) - 1 EXTRA CREDIT (2 pts) Evaluate the following integral cos( x ) + 3 x 2-p dx cos( x ) + 3 x- 2-p ( ) dx = sin( x ) + 3 x- 1- 1-px + c = sin( x ) -3 x-px + c...
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