Limits And Continuity — Chapter Summary

The limit of a function f(x)

The limit of a function f(x) as x approaches 'a' is the value that f(x) gets closer to as x gets arbitrarily close to 'a', regardless of whether f(a)

The left

The left-hand limit (LHL) is the value f(x) approaches as x approaches 'a' from the left (x → a⁻). The right-hand limit (RHL) is the value as x approa

A function f(x) is continuous at

A function f(x) is continuous at x = a if three conditions are met: (1) f(a) is defined, (2) the limit of f(x) as x → a exists, and (3) the limit equa

Standard limits like lim (x→0) sinx/x

Standard limits like lim (x→0) sinx/x = 1 and lim (x→0) (eˣ - 1)/x = 1 are used frequently. L'Hospital's Rule helps evaluate indeterminate forms like