Let's define the function . Note that the polynomial that you obtain is one degree less than the third argument. The remainder is denoted, in general, by . , in this context, stands for a sum of terms of order at least n in , that is, terms containing in the power of at least n. Note the proper use of parentheses. Usually when plotting functions we have to worry about the x-range only.
Maple adjusts the y-range automatically, so the whole graph is visible.
It doesn't work very well if a function has a vertical asymptote, as has at . In such cases it may be a good idea to specify the range for y, as well. The proper syntax looks as follows. We see the thicker, black graph of the original function and the graphs of the first two polynomials. Maple displays also the vertical asymptote .