Limits and continuity

Concepts

• Continuous function from Calculus 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 from Calculus 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 from Calculus 20 exercisesIf f is continuous on a closed and bounded interval [a,b], then f attains an absolute maximum and minimum on [a,b].
• Limit of a function from Calculus 20 exercisesThe limit of f as x approaches a is L if f(x) gets as close to L as we like when x is taken sufficiently close to a, regardless o…
• Sequential continuity 10 exercisesA function f is sequentially continuous at c if, for every sequence (x_n) in the domain converging to c, the sequence of images f…
• Uniform continuity 10 exercisesA function f is uniformly continuous on a set A if for each ε>0 there is a δ>0, valid for all points at once, that controls |f(x)…