Limits, continuity and L’Hôpital’s rule

By the end you’ll be able to

• Evaluate one-sided limits, limits at infinity and limits of algebraic, trigonometric, exponential and logarithmic expressions
• Resolve the indeterminate forms 0/0, ∞/∞, 0·∞, ∞ − ∞, 1^∞, 0^0 and ∞^0 using L’Hôpital’s rule, algebraic manipulation, logarithms or Taylor expansions
• Apply standard limits such as $\lim_{x\to 0} \frac{\sin x}{x} = 1$ and $\lim_{n\to\infty}(1 + a/n)^n = e^a$, and compare growth rates of logarithms, powers, exponentials and factorials