∫

Limit

High School

Definition

The value a function approaches as the variable approaches some value.

lim_x → a f(x) = L

f(x) approaches L as x approaches a

lim_x → ∈fty (1)/(x) = 0

Limit as x approaches infinity

Example 1

Find lim(x→2) (x² - 4)/(x - 2).

lim_x → 2 (x² - 4)/(x - 2) = lim_x → 2 (x+2) = 4

Example 2

Find lim(x→∞) (3x² + x)/(x² + 1).

lim_x → ∈fty (3x² + x)/(x² + 1) = 3

Discovered by: Augustin-Louis Cauchy, Karl Weierstrass (19th century)

The rigorous ε-δ definition was established by Weierstrass.

Definition of derivative

Definition of definite integral