How to calculate the highest degree term with its coefficient in this expression with respect to t?

syms t x;

expression = ((49*t^2 - 82600*t + 35060000)^(1/2)/550)*x;

Answer 1

[Star Strider]

I am not certain that what you want to do is possible.

The closest I could get to it is to use a taylor series approximation —

syms t x;
expression = ((49*t^2 - 82600*t + 35060000)^(1/2)/550)*x;

ts = taylor(expression, t, 'Order',3)

ts = 

[coef,term] = coeffs(ts)

coef = 

term = 

coef(1)

ans = 

vpa(coef(1), 7)

ans = 

5.364454e-8

term(1)

ans = 

ps = series(expression, t, 'Order',3)

ps = 

The Puiseux series expansion produces the same result (as would be expected in this instance).

.

Answer 2

[Matt J]

syms t x;
expression = ((49*t^2 - 82600*t + 35060000)^(1/2)/550)*x;


p=sym2poly((expression*550/x)^2)

p = 1×3

49 -82600 35060000

degree=numel(p)

degree = 3

coeff=p(1)

coeff = 49