Debug Info:
{
  "title": "Limit",
  "symbol": "lim",
  "definition": "The limit of a function is the value that the function approaches as the input (usually x) approaches a certain value.",
  "usage": "The limit of f(x) as x approaches a is written as lim(x→a) f(x).",
  "examples": [
    {
      "description": "Limit of sin(x)/x as x approaches 0",
      "latex": "\\lim_{x \\to 0} \\frac{\\sin(x)}{x} = 1"
    },
    {
      "description": "Limit definition of e",
      "latex": "e = \\lim_{n \\to \\infty} (1 + \\frac{1}{n})^n"
    }
  ],
  "tags": [
    "calculus",
    "analysis",
    "convergence"
  ],
  "relatedConcepts": [
    "continuity",
    "derivative",
    "infinite series"
  ]
}

Limit

Symbol

lim

Definition

The limit of a function is the value that the function approaches as the input (usually x) approaches a certain value.

Usage

The limit of f(x) as x approaches a is written as lim(x→a) f(x).

Examples

Description: Limit of sin(x)/x as x approaches 0

LaTeX: \lim_{x \to 0} \frac{\sin(x)}{x} = 1
Description: Limit definition of e

LaTeX: e = \lim_{n \to \infty} (1 + \frac{1}{n})^n

Tags