gibson:teaching:fall-2014:math445:lab4
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gibson:teaching:fall-2014:math445:lab4 [2014/10/21 10:55] gibson |
gibson:teaching:fall-2014:math445:lab4 [2014/10/25 05:01] gibson |
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| - Use a ''for'' loop to perform the Newton-search iteration. Take up to ten Newton steps. | - Use a ''for'' loop to perform the Newton-search iteration. Take up to ten Newton steps. | ||
| - | - Use a ''if'' statement inside the ''for'' loop to test if either $|f(x)| < \epsilon$ or $|dx| < \epsilon$. If so, use a ''break'' statement to terminate the iteration and return from the function. For our purposes ''1e-07'' is a decent choice for the value of tolerance $\epsilon$. | + | - Use a ''if'' statement inside the ''for'' loop to test if either $|f(x)| < 2 \epsilon$ or $|dx| < \epsilon$. If so, use a ''break'' statement to terminate the iteration and return from the function. For our purposes ''1e-07'' is a decent choice for the value of tolerance $\epsilon$. |
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| **(b)** Find the cube root of 54. (Hint: devise an equation whose answer is $x = \sqrt[3]{72}$.) | **(b)** Find the cube root of 54. (Hint: devise an equation whose answer is $x = \sqrt[3]{72}$.) | ||
| - | **%%(c)%%** Find an ''x'' for which $\sqrt{4-x^2} = x \tan x$. | + | **%%(c)%%** Find an ''x'' for which $\sqrt{3-x^2} = x \tan x$. |
| Hint: find good initial guesses for the Newton search by plotting each function and roughly | Hint: find good initial guesses for the Newton search by plotting each function and roughly | ||
gibson/teaching/fall-2014/math445/lab4.txt ยท Last modified: 2014/10/25 05:01 by gibson
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