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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

예제 1★★★☆☆

Find lim(x→2) (x² - 4)/(x - 2).

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

예제 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

#analysis#calculus#limit#fundamental