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Unformatted text preview: MAT 2384Practice Problems on ﬁxedpoint iteration, Newton’s Methods and Secant method 1. Apply ﬁxedpoint iteration to ﬁnd the root of sin x − 1x4 = 0 in the interval 1, . sequence are satisﬁed. 2. Apply ﬁxedpoint iteration to ﬁnd the root of x4 − x + 0.2 = 0 near x = 0 to 5 decimal places. Use x0 = 0. 3. Apply ﬁxedpoint iteration to ﬁnd the smallest positive solution of sin x = e−0.5x in the interval [0.1, 1] to 5 decimal places. Use x0 = 1 and make sure that the conditions for convergence of the iteration sequence are satisﬁed. 4. Use Newton’s Method (6 decimal accuracy) to solve sin x = cotx. Use x0 = 1. First sketch the functions. 5. Use Newton’s Method (6 decimal accuracy) to ﬁnd a root of x3 − 5x + 3 in the interval [1, 2]. Use x0 = 2. First sketch the function. 6. Use Newton’s Method (6 decimal accuracy) to compute √ 5 2. Use x0 = 1
π 2 to 4 decimal places. Use x0 = 1.4 and make sure that the conditions for convergence of the iteration 7. Use the secant method with x0 = 1, x1 = 0.7 to ﬁnd a solution to the equation e−x − tan x = 0 to 5 decimal places. 1 ...
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 Fall '09
 josephkhoury

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