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

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?

Answer 1

[Walter Roberson]

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.