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2. Squeeze theorem - Wikipedia

   en.wikipedia.org/wiki/Squeeze_theorem

   Indeed, if a is an endpoint of I, then the above limits are left- or right-hand limits. A similar statement holds for infinite intervals: for example, if I = (0, ∞), then the conclusion holds, taking the limits as x → ∞. This theorem is also valid for sequences. Let (a n), (c n) be two sequences converging to ℓ, and (b n) a sequence.

3. Limit of a function - Wikipedia

   en.wikipedia.org/wiki/Limit_of_a_function

   In particular, one can no longer talk about the limit of a function at a point, but rather a limit or the set of limits at a point. A function is continuous at a limit point p of and in its domain if and only if f ( p ) is the (or, in the general case, a ) limit of f ( x ) as x tends to p .

4. Limit (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Limit_(mathematics)

   On one hand, the limit as n approaches infinity of a sequence {a n} is simply the limit at infinity of a function a(n) —defined on the natural numbers {n}. On the other hand, if X is the domain of a function f ( x ) and if the limit as n approaches infinity of f ( x n ) is L for every arbitrary sequence of points { x n } in X − x 0 which ...

5. Limit inferior and limit superior - Wikipedia

   en.wikipedia.org/wiki/Limit_inferior_and_limit...

   Assume that the limit superior and limit inferior are real numbers (so, not infinite). The limit superior of is the smallest real number such that, for any positive real number , there exists a natural number such that < + for all >. In other words, any number larger than the limit superior is an eventual upper bound for the sequence.

6. List of limits - Wikipedia

   en.wikipedia.org/wiki/List_of_limits

   This is a list of limits for common functions such as elementary functions. In this article, the terms a , b and c are constants with respect to x . Limits for general functions

7. Calculus - Wikipedia

   en.wikipedia.org/wiki/Calculus

   Limits describe the behavior of a function at a certain input in terms of its values at nearby inputs. They capture small-scale behavior using the intrinsic structure of the real number system (as a metric space with the least-upper-bound property). In this treatment, calculus is a collection of techniques for manipulating certain limits.

8. Uniform convergence - Wikipedia

   en.wikipedia.org/wiki/Uniform_convergence

   A sequence of functions () converges uniformly to when for arbitrary small there is an index such that the graph of is in the -tube around f whenever . The limit of a sequence of continuous functions does not have to be continuous: the sequence of functions () = ⁡ (marked in green and blue) converges pointwise over the entire domain, but the limit function is discontinuous (marked in red).

9. L'Hôpital's rule - Wikipedia

   en.wikipedia.org/wiki/L'Hôpital's_rule

   L'Hôpital's rule (/ ˌ l oʊ p iː ˈ t ɑː l /, loh-pee-TAHL) or L'Hospital's rule, also known as Bernoulli's rule, is a mathematical theorem that allows evaluating limits of indeterminate forms using derivatives.