One way to compute the exponential function e* is to truncate its Taylor series expansion around...

 

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One way to compute the exponential function e* is to truncate its Taylor series expansion around x = 0, 1 et = 1+x+ 2! 1 3! Unfortunately, many terms are required for accuracy if |x| is large. But a special property of the exponential is that e2x = (e*)². This leads to a scaling and squaring method: Divide x by 2 repeatedly until |x| < 1/2, use the Taylor series (16 terms should be more than enough), and square the result repeatedly. Write a function expss (x) that performs these three steps. (The functions cumprod and polyval can help with evaluating the Taylor expansion.) Test your function on x values -30, -3, 3, 30. One way to compute the exponential function e* is to truncate its Taylor series expansion around x = 0, 1 et = 1+x+ 2! 1 3! Unfortunately, many terms are required for accuracy if |x| is large. But a special property of the exponential is that e2x = (e*)². This leads to a scaling and squaring method: Divide x by 2 repeatedly until |x| < 1/2, use the Taylor series (16 terms should be more than enough), and square the result repeatedly. Write a function expss (x) that performs these three steps. (The functions cumprod and polyval can help with evaluating the Taylor expansion.) Test your function on x values -30, -3, 3, 30.

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