The properties of limits can be used to perform operations on the limits of functions rather than the functions themselves. See
[link] .
The limit of a polynomial function can be found by finding the sum of the limits of the individual terms. See
[link] and
[link] .
The limit of a function that has been raised to a power equals the same power of the limit of the function. Another method is direct substitution. See
[link] .
The limit of the root of a function equals the corresponding root of the limit of the function.
One way to find the limit of a function expressed as a quotient is to write the quotient in factored form and simplify. See
[link] .
Another method of finding the limit of a complex fraction is to find the LCD. See
[link] .
A limit containing a function containing a root may be evaluated using a conjugate. See
[link] .
The limits of some functions expressed as quotients can be found by factoring. See
[link] .
One way to evaluate the limit of a quotient containing absolute values is by using numeric evidence. Setting it up piecewise can also be useful. See
[link] .
Section exercises
Verbal
Give an example of a type of function
whose limit, as
approaches
is
If
is a polynomial function, the limit of a polynomial function as
approaches
will always be
When direct substitution is used to evaluate the limit of a rational function as
approaches
and the result is
does this mean that the limit of
does not exist?
What does it mean to say the limit of
as
approaches
is undefined?
It could mean either (1) the values of the function increase or decrease without bound as
approaches
or (2) the left and right-hand limits are not equal.
The amount of money in an account after
years compounded continuously at 4.25% interest is given by the formula
where
is the initial amount invested. Find the average rate of change of the balance of the account from
year to
years if the initial amount invested is $1,000.00.
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