I am asking my mentor for my class about this question, but unfortunately the answers I get from her often take forever and do not always clear things up for me, so I hope someone out there in Physics Forum has a good way of explaining this to me. Here goes... The question has some Mathematica input (Normal[Series] command) and output for the function f(x) = e -xCos(x). Then the question is asked "Mathematica is trying to tell you that, at x = 0, e-x Cos[x] and 1 - x + (x3)/3 - (x4)/6 + (x5)/5 have order of contact ____?" Now to answer, I went back to what we learned about the definition of an expansion in powers of x was. This definition from the materials is: Given a function f[x], the expansion of f[x] in powers of x is: a + ax + a2[x]2 + ... + a[k]xk, where the numbers a, a, a, ..., a[k] are chosen such that for every positive integer m, the function f[x] and the polynomial a + ax + ax2 + ... + a[m]xm have order of contact m at x = 0. From this definition, I believed the answer to the question would be "5" because we see that in the expansion given, we have a 5th degree polynomial. Instead, the answer was 4. Can you please explain where my reasoning was faulty, and why the actual answer is 4? My guess is that the (x5)/5 term is actually xm+1making it a 5th degree polynomial where m = 4. Is that correct? Or am I barking up the wrong tree? Thank you for your help!