Chapter 3 - Limits & Continuity - Instant Flashcards
A ….. is an interval that includes all of its limit points.
closed interval
A closed interval is an interval that … .
includes all of its limit points.
An ….. is an interval that does not include its end points.
open interval
An open interval is an interval that … .
does not include its end points
The interval (a, b) denotes … .
an open interval
The [a, b] denotes … .
a closed interval
An interval with the endpoints +/- ∞ is denoted by … .
(-∞, ∞ )
An interval in which one endpoint is included but not the other is called … .
half-closed interval
What is the limit of a function?
The limit of a function f(x) is a value L (if it exists), to which the function f(x) gets arbitrarily close to, when x approaches c.
What are the two ways a limit can be denoted?
What is a right-hand limit?
A limit, when x tends to c from the right hand side.
What is a left-hand limit?
A limit, when x tends to c from the left.
Which condition has to be satisfied, so that a limit exists?
Right hand limit equals left hand limit.
When calculating a limit,
which value are we not allowed to substitute instead of x?
∞
When dealing with limits as x -> ∞, which property can be used.
Define the addition property of limits.
State the multiplication property of limits.
State the division property of limits.
State the composition property of limits.
