L’Hospital’s Rule allows for the evaluation of the limits of fractions that reduce to indeterminate forms, i.e. these:
Essentially, we can solve these limits by dividing the derivatives of the numerator by the derivative of the denominator. For a layman such as myself, and the many that have come before me since L’Hospital’s Rule was first published in 1696, this comes in very handy.
Although attributed to Guillaume de l’Hôpital, it was actually introduced to him by Johann Bernoulli. Bernoulli was a mathematical heavyweight who began studying math seriously as a hobby while studying medicine formally at the university. So he and I have something in common, inasmuch as we both have taken up this beautiful pursuit on our own, rather than through formalized study.
Obviously Bernoulli was on an entirely different strata, having made serious contributions to the historical arch of mathematics, including L’Hospital’s Rule, and tutoring none other than the great Leonard Euler in his childhood. Nevertheless, it’s encouraging to see what progress others have made through setting themselves to the path of learning.