I have a question about this, but I'm pretty sure I know the answer.

"For the polynomial f(x) = x^2 - x^4 + 2x^3 - 13 as x - oo, f(x) - oo"
True or false?

I'm just not sure if the leading coefficient is x^2 or if it should be - x^4.

Question

I have a question about this, but I'm pretty sure I know the answer.

"For the polynomial f(x) = x^2 - x^4 + 2x^3 - 13 as x -> oo, f(x) -> oo"
True or false?

I'm just not sure if the leading coefficient is x^2 or if it should be - x^4.

anonymous · Answer

But if the leading coefficient is -x^4, then it is false, and if the leading coefficient is x^2, then it is true.

anonymous · Answer

@phi you're usually of much help to me, can you help out?

anonymous · Answer

@amistre64 ?

anonymous · Answer

I just simply need to know which one needs to be the leading coefficient?

ranga · Answer

The polynomial should be put in order first: from highest degree term to the lowest.  The leading term will be -x^4.

amistre64 · Answer

"leading" coefficient is a matter of form and really misses the point of it.

When x gets very big, the control of the function is held by the terms of largest degree no matter where that term is placed in the setup