Assertion: function's limit | /r/HasProperty | equal
Facets:
value: to l.
type: OTHER
value: to 42
type: OTHER
value: to f(p
type: OTHER
Source sentences:
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: if and only if both the right-handed limit and left-handed limit of f at p exist and are equal to L.
text: if and only if both the right-handed limit and left-handed limit of f at p exist and are equal to L.
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: The limit of x2 as x approaches 4 is equal to 42.
text: And so for a function to be continuous at x = c, the limit must exist as x approaches c, that is, the left- and right-hand limits -- those numbers -- must be equal.
text: Since v(t) is a continuous function, then the limit as t approaches 5 is equal to the value of v(t) at t = 5.