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Mathematics vocabulary · Calculus

Continuous

Meaning in mathematics, with examples

/kənˈtɪnjuəs/adjectiveCommon term

In mathematics, continuous means: Having no breaks, jumps or holes; a function is continuous at a point if its limit there equals its value, so its graph can be drawn without lifting the pen.

In Turkish: sürekli

How it is used

You say a function is 'continuous at x = a' or 'continuous on an interval'. The opposite is 'discontinuous', and the point where it happens is a 'discontinuity'. Every differentiable function is continuous, but not every continuous function is differentiable.

Example sentences

  1. Show that the function is continuous at x = 2.

  2. The function |x| is continuous everywhere, but it has no derivative at zero.

Common collocations

  • continuous at a point
  • continuous function
  • continuous on an interval
  • piecewise continuous
  • limitThe value that a function or sequence gets closer and closer to as the input approaches a certain number or grows without bound.
  • derivativeA function that gives the rate of change of another function at each point, which is the slope of its graph there; the derivative of x² is 2x.
  • functionA rule that takes each input from a set and gives exactly one output, for example f(x) = 2x + 1, which doubles a number and adds one.
  • graphA drawing that shows the relationship between quantities, especially all the points (x, y) of a function shown on a pair of axes.

More terms: Calculus

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