1.2-a Computers can only add, subtract, multiply and divide. So, how do they calculate a function...

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1.2-a Computers can only add, subtract, multiply and divide. So, how do they calculate a function such as sin(x)? They convert the function to a polynomial using its Taylors Expansion. Remember, given a differential function f(x), its Taylor's polynomial approximation at x=h is: f" (h) f(x) = f(h) + f'(h)(x − h) + - (xh)² + ... 2! Use the MATLAB function taylortool('sin(x)') to study the Taylor Series Approximation of a sin function. • Find the Taylor expansion of ex. (Use exp(x) in MATLAB) • Find the Taylor expansion of sin²(x). How many terms N do you need for a good approximation? 1.2-a Computers can only add, subtract, multiply and divide. So, how do they calculate a function such as sin(x)? They convert the function to a polynomial using its Taylors Expansion. Remember, given a differential function f(x), its Taylor's polynomial approximation at x=h is: f" (h) f(x) = f(h) + f'(h)(x − h) + - (xh)² + ... 2! Use the MATLAB function taylortool('sin(x)') to study the Taylor Series Approximation of a sin function. • Find the Taylor expansion of ex. (Use exp(x) in MATLAB) • Find the Taylor expansion of sin²(x). How many terms N do you need for a good approximation?

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