Infinitesimal calculus MOC

Limits

Intuitively (for the formal definition, see Epsilon-Delta Construction of the Limit), a limit of function as approaches

is what gets close to as gets close to . In some cases this is obvious — for example, for any function Continuous and defined at ,

In other cases, it may be a value which the function visibly approaches

Limits can be calculated using Limit Laws. They are generalised by the category-theoretic notion of Limits and colimits

One-sided limits

Limits can be defined as approaching from the left hand side (), or as approaching from the right hand side (). These are written as and respectively. Hence,

Undefined limits

Limits Do Not Exist (DNE) in cases where

1. For a bilateral limit, and give different results (see above).
2. The limit is .
3. The input limit (i.e. what approaches) is a finite distance outside the domain of .

Multivariable limits

See Multivariable limits.

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