Continuity

Concepts

• Continuous function 20 exercisesA function f is continuous at a if f(a) is defined, its limit as x tends to a exists and equals f(a).
• Intermediate value theorem 20 exercisesIf f is continuous on [a,b] and N lies between f(a) and f(b), there is some c∈(a,b) with f(c)=N.
• Extreme value theorem 20 exercisesIf f is continuous on a closed and bounded interval [a,b], then f attains an absolute maximum and minimum on [a,b].
• Types of discontinuity 10 exercisesA function is discontinuous at a when some continuity condition fails. It can be removable, a jump, or infinite.
• Composition and inverse from Set theory 30 exercisesThe composition g∘ f applies f first and then g. The inverse f^-1 exists when f is bijective and undoes its action.