Limits

Concepts

• Limit of a function 20 exercisesThe limit of f as x approaches a is L if f(x) gets as close to L as we like when x is taken sufficiently close to a, regardless o…
• One-sided limits 10 exercisesThe left-hand limit uses only values x<a and the right-hand limit only values x>a. The limit of f at a exists if and only if both…
• Limit laws 10 exercisesIf lim _x→ a f(x) and lim _x→ a g(x) exist, the limit of their sum, difference, product or quotient (with nonzero denominator) is…
• Indeterminate forms 10 exercisesAn indeterminate form is a limit expression, such as (0)/(0) or (∞)/(∞), whose value cannot be deduced from the limits of its par…
• Squeeze theorem 10 exercisesIf g(x)≤ f(x)≤ h(x) near a and g and h both have limit L at a, then f also has limit L at a.
• Special trigonometric limits 11 exercisesTwo basic limits in radians: (sin x)/(x) tends to 1 and (1-cos x)/(x) tends to 0 as x tends to 0.
• Limits at infinity 10 exercisesThe limit of f as x tends to infinity describes what happens to f(x) when x grows without bound. For a quotient of polynomials, t…
• Asymptotes 10 exercisesAn asymptote is a line the graph approaches without touching it. The line x=a is vertical if f tends to pm∞ as x→ a; the line y=L…