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.
What is the limit of x2 as x -> ∞?
The limit is not ∞.
The limit does not exist.
What are the four Properties of limits?
The additon property, the multiplication property, the division property,
and the composition property.
Define the addition property of limits.
State the multiplication property of limits.
State the division property of limits.
State the composition property of limits.
Generally what is the best strategy,
if you need to calculate the limit as x -> ∞,
and your function is of the form two polynomials by each other.
Dividing numerator and denominator by the highest power of x
that you can see in that function.
