Using Taylor Expansions: how to impose 'large' approximations, i.e., "for large x"?

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HC98
HC98 on 5 Apr 2021
Answered: Walter Roberson on 5 Apr 2021
Say I have a function:
and I want to see what happens in the region of large x, i.e., I Taylor expad f(x) in the region of large x and see how the functiuon changes. I Can do this on paper but how do I instruct matlab to take x as being say x>>a where a is small?

Answers (1)

Walter Roberson
Walter Roberson on 5 Apr 2021
format long g
syms alpha x
f = sin(alpha*x)
f = 
fapprox(x) = taylor(f, x, 10000, 'order', 20)
fapprox(x) = 
fapprox(3183*pi)
ans = 
fapprox_tenth(x) = simplify(subs(ans, alpha, 1/10))
fapprox_tenth(x) = 
fapprox_tenth(3183*pi)
ans = 
vpa(ans)
ans = 
0.80901699437494742410229341718282
sin(3183*pi*1/10)
ans =
0.809016994374915
That's a pretty good approximation
sin(10*3183*pi*1/10)
ans =
9.49298408281609e-14
vpa(fapprox_tenth(10*3183*pi))
ans = 
0.80901699437494742410229341718282
but that is not.

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