Examples for

Continuity

A function is continuous at a point when the value of the function equals its limit. Discontinuities can be seen as "jumps" on a curve or surface. The sum, difference, product and composition of continuous functions are also continuous. Wolfram|Alpha can determine the continuity properties of general mathematical expressions, including the location and classification (finite, infinite or removable) of points of discontinuity.

Continuity

Find where a function is continuous or discontinuous.

Determine whether a function is continuous:

Is f(x)=x sin(x^2) continuous over the reals?
is sin(x-1.1)/(x-1.1)+heaviside(x) continuous

Determine continuity at a given point:

is tan(x) continuous at pi?
is 1/(x^2-1)+UnitStep[x-2]+UnitStep[x-9] continuous at x=9

Discontinuities

Find where functions are discontinuous.

Locate discontinuities of a function:

discontinuities (x^3+8)/(x^3+3x^2-4x-12)
discontinuities of sec(x)tan(x)

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Step-by-Step Solutions for Calculus

RELATED EXAMPLES

  • Calculus & Analysis
  • Limits
  • Mathematical Functions
  • Topology