Assertion: limit | /r/HasProperty | equal
Facets:
value: to the limit
type: OTHER
value: to 1
type: OTHER
value: to their common value
type: OTHER
value: to f(p
type: OTHER
value: including the infinities
type: OTHER
value: to l.
type: OTHER
Source sentences:
text: The limit, as x approaches infinity, of 1/ x - 2 is therefore equal to -2.
text: If these limits exist at p and are equal there, then this can be referred to as the limit of f(x) at p.
text: → p exists and is equal to L if, for all subsets Ω of X with limit point p, the limit of the restriction of f to Ω exists and is equal to L.
text: and are equal, the limit is the leading coefficient of divided by the leading coefficient of ;
text: The function f is continuous at p if and only if the limit of f(x) as x approaches p exists and is equal to f(p).
text: As in the case for sequences, the limit inferior and limit superior are always well-defined if we allow the values +∞ and -∞; in fact, if both agree then the limit exists and is equal to their common value (again possibly including the infinities).
text: Therefore, the limit inferior and limit superior of the net are equal to the limit superior and limit inferior of B {\displaystyle B} respectively.
text: Therefore, the limit inferior and limit superior of the sequence are equal to the limit superior and limit inferior of C {\displaystyle C} respectively.
text: In other words, the two equations give identical values except at \(x = 2\) and because limits are only concerned with that is going on around the point \(x = 2\) the limit of the two equations will be equal.
text: then the limit as x becomes infinite is equal to the quotient of the leading coefficients.
text: When the base is set to e, this limit is equal to 1, and so e is symbolically defined by the equation: