So basically I'm doing my first year of a natural sciences undergraduate course, and I came up against this series of questions.
"Approximate the following functions in the limit $|x| << 1.$ In each case give the leading term and order of the error."
So, how would I go about doing that, for instance with the function: $$f(X)=\frac{X^3+X}{X+8} ?$$ I could tell you that as $x\to 0$ this function $f(X) \to 0,$ but that's about it.
I think my biggest problem is that I'm not actually sure what it means by 'leading term' and 'order of error'.
I've met big O notation briefly, it was explained as "$\lim_{x \to a} f(x) = O(g(x))$ if $f(x)$ and $g(x)$ look the same around a."
I assume it relates to that, but I can find nothing among my lecture notes nor on Google as to what this question actually wants from me, so if somebody could explain, that would be great! Thanks!