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# HW1 - = x and y = 2 sin x(b Use the Bisection method to Fnd...

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Math 151A HW #1, due Friday, January 12 - Reading: sections 1.1, 1.3, 1.4 and the matlab code given below (com- pare with algorithm 2.1. from the textbook, page 47). - Problems from section 2.1: #1 (with a hand calculator), #2(a) (with a hand calculator), #7(ab), #12, #15 (for the longer calculations, you can use one of the codes posted on the class webpage). #1 Use the Bisection method to find p 3 for f ( x ) = x - cos x on [0 , 1]. #2(a) Let f ( x ) = 3( x + 1)( x - 1 2 )( x - 1). Use the Bisection method on the following intervals to find p 3 : (a) [ - 2 , 1 . 5] #7 (a) Sketch the graphs of
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Unformatted text preview: = x and y = 2 sin x . (b) Use the Bisection method to Fnd an approximation to within 10-5 to the Frst positive value of x with x = 2 sin x . #12 ±ind an approximation to √ 3 correct to within 10-4 using the Bi-section Algorithm (hint: consider f ( x ) = x 2-3). #15 ±ind a bound for the number of iterations needed to achieve an approximation with accuracy 10-4 to the solution of x 3-x-1 = 0 lying in the interval [1 , 2]. ±ind an approximation to the root with this degree of accuracy. 1...
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