Limits and Series

Limits

limit(sin(x)/x, x = 0);        # 1
limit(1/x, x = infinity);      # 0

Taylor series

taylor(exp(x), x = 0, 5);

Gives the Taylor expansion of e^x around x = 0, up to the 5th-order term -- the exact polynomial approximation, with every coefficient as an exact fraction.

Why This Matters for Your Exams

A Taylor series question is really just asking you to apply diff repeatedly and plug into the formula -- Maple's taylor does that bookkeeping for you so you can check your by-hand working.