Computing series in MATLAB

Hello!

I wonder if it is possible somehow to force MATLAB to compute ANY series for this function: ((4+3x)/(x+2))^(2x-1) as x->inf. I need to find the limit without using the limit function in MATLAB.

I tried some ways, but they don't appear to be working as MATLAB says there is an error.

I would be very thankful for your help!

[Rick Rosson]

Please post your code and the exact error message.

[Svetlana]

Firstly, I tried to compute a Taylor series so I've made a substitution: t = 1/x, t->0

g = ((3/t + 4)/(1/t + 2))^(2/t - 1)

taylor(g)

Warning: Cannot compute a Taylor expansion of '((3/t + 4)/(1/t + 2))^(2/t - 1)'. Try 'series' with the 'Left', 'Right', or 'Real' option for a more general expansion. [taylor]

or:

f = ((3/t + 4)/(1/t + 2))^(2/t - 1)

series(f, t = 0, Left)

Error: The expression to the left of the equals sign is not a valid target for an assignment.

Answer 1

[Roger Stafford]

The reason you're having trouble finding that limit is that there is no finite limit! The expression goes quickly to infinity as x approaches infinity. For the same reason the expression

   ((3/t + 4)/(1/t + 2))^(2/t - 1)

has no Taylor series because it has a singularity at t = 0. It approaches infinity from the right and zero from the left.