• Continuity Equation
• Continuity Of Care
• Continuity Synonym

1. Continuity (countable and uncountable, plural continuities) Lack of interruption or disconnection; the quality of being continuous in space or time. Considerable continuity of attention is needed to read German philosophy. (uncountable, mathematics) A characteristic property of a continuous function.
2. Definition for continuity. And the general idea of continuity, we've got an intuitive idea of the past, is that a function is continuous at a point, is if you can draw the graph of that function at that point without So what do we mean by that?

Continuity (mathematics), the opposing concept to discreteness; common examples include Continuous probability distribution or random variable in probability and statistics Continuous game, a generalization of games used in game theory Law of Continuity, a heuristic principle of Gottfried Leibniz. For problems 3 – 7 using only Properties 1 – 9 from the Limit Properties section, one-sided limit properties (if needed) and the definition of continuity determine if the given function is continuous or discontinuous at the indicated points. F (x) = 4x+5 9 −3x f (x) = 4 x + 5 9 − 3 x x = −1 x = − 1 x = 0 x = 0.

Continuity or continuous may refer to:

Mathematics[edit]

• Continuity (mathematics), the opposing concept to discreteness; common examples include
  • Continuous probability distribution or random variable in probability and statistics
  • Continuous game, a generalization of games used in game theory
  • Law of Continuity, a heuristic principle of Gottfried Leibniz
• Continuous function, in particular:
  • Continuity (topology), a generalization to functions between topological spaces
  • Scott continuity, for functions between posets
  • Continuity (set theory), for functions between ordinals
  • Continuity (category theory), for functors
  • Graph continuity, for payoff functions in game theory
• Continuity theorem may refer to one of two results:
  • Lévy's continuity theorem, on random variables
  • Kolmogorov continuity theorem, on stochastic processes
• In geometry:
  • Parametric continuity, for parametrised curves
  • Geometric continuity, a concept primarily applied to the conic sections and related shapes

Continuity Equation

Science[edit]

• Continuity equations applicable to conservation of mass, energy, momentum, electric charge and other conserved quantities
• Continuity test for an unbroken electrical path in an electronic circuit or connector
• In materials science:
  • a colloidal system, consists of a dispersed phase evenly intermixed with a continuous phase
  • a continuous wave, an electromagnetic wave of constant amplitude and frequency

Entertainment[edit]

• Continuity (broadcasting), messages played by broadcasters between programs
• Continuity editing, a form of film editing that combines closely related shots into a sequence highlighting plot points or consistencies
• Continuity (fiction), consistency of plot elements, such as characterization, location, and costuming, within a work of fiction (this is a mass noun)
• Continuity (setting), one of several similar but distinct fictional universes in a broad franchise of related works (this is a count noun)

Continuity Of Care

Other uses[edit]

• Continuity (Apple), a set of features introduced by Apple
• Continuous and progressive aspects in linguistics
• Continuity in architecture (part of complementary architecture)

See also[edit]

Continuity Synonym

Section 2-9 : Continuity

1. The graph of (fleft( x right)) is given below. Based on this graph determine where the function is discontinuous. Solution
2. The graph of (fleft( x right)) is given below. Based on this graph determine where the function is discontinuous. Solution

For problems 3 – 7 using only Properties 1 – 9 from the Limit Properties section, one-sided limit properties (if needed) and the definition of continuity determine if the given function is continuous or discontinuous at the indicated points.

1. (displaystyle fleft( x right) = frac{{4x + 5}}{{9 - 3x}})
   1. (x = - 1)
   2. (x = 0)
   3. (x = 3)
   Solution
2. (displaystyle gleft( z right) = frac{6}{{{z^2} - 3z - 10}})
   1. (z = - 2)
   2. (z = 0)
   3. (z = 5)
   Solution
3. (gleft( x right) = left{ {begin{array}{rl}{2x}&{x < 6}{x - 1}&{x ge 6}end{array}} right.)
   1. (x = 4)
   2. (x = 6)
   Solution
4. (hleft( t right) = left{ {begin{array}{rl}{{t^2}}&{t < - 2}{t + 6}&{t ge - 2}end{array}} right.)
   1. (t = - 2)
   2. (t = 10)
   Solution
5. (gleft( x right) = left{ {begin{array}{rc}{1 - 3x}&{x < - 6}7&{x = - 6}{{x^3}}&{ - 6 < x < 1}1&{x = 1}{2 - x}&{x > 1}end{array}} right.)
   1. (x = - 6)
   2. (x = 1)
   Solution

For problems 8 – 12 determine where the given function is discontinuous.

1. (displaystyle fleft( x right) = frac{{{x^2} - 9}}{{3{x^2} + 2x - 8}}) Solution
2. (displaystyle Rleft( t right) = frac{{8t}}{{{t^2} - 9t - 1}}) Solution
3. (displaystyle hleft( z right) = frac{1}{{2 - 4cos left( {3z} right)}}) Solution
4. (displaystyle yleft( x right) = frac{x}{{7 - {{bf{e}}^{2x + 3}}}}) Solution
5. (gleft( x right) = tan left( {2x} right)) Solution

For problems 13 – 15 use the Intermediate Value Theorem to show that the given equation has at least one solution in the indicated interval. Note that you are NOT asked to find the solution only show that at least one must exist in the indicated interval.

1. (25 - 8{x^2} - {x^3} = 0) on (left[ { - 2,4} right]) Solution
2. ({w^2} - 4ln left( {5w + 2} right) = 0) on (left[ {0,4} right]) Solution
3. (4t + 10{{bf{e}}^t} - {{bf{e}}^{2t}} = 0) on (left[ {1,3} right]) Solution