Limits in Differential Equations

  1. Why we cannot use inscribed polyhedrons to approximate the area of a curved surface [Cou2, vol.2, p.421, l.-10-p.422, l.16; p.540, l.-14-p.542, l.12].

  2. The indeterminate form 0: Finding the sum of an infinite number of terms, where each term is infinitesimal.
    Example. lim n + (1 - 1/(2n) + 1/(3n2) - ) [Wat1, p.584, l.17].
        We may regard the series as the power series of the analytic function
    f (t) = [log (1+t)]/t.
    Then lim t0 f (t) = f (0) since an analytic function is continuous.