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Example Questions
Example Question #461 : Derivative Review
Define
.Find
.
First, find
as follows:
Therefore,
.Now, find
as follows:
Example Question #461 : Derivatives
Define
.Find
.
First, find
as follows:
Therefore,
.Now, find
as follows:
Example Question #1591 : Calculus Ii
Define
.Find
.
First, find
as follows:
Therefore,
.Now, find
as follows:
Example Question #462 : Derivatives
Let the initial approximation of a solution of the equation
be
.Use one iteration of Newton's method to find an approximation for
. Give your answer to the nearest thousandth.
Rewrite the equation to be solved for
as .Let
.
The problem amounts to finding a zero of
. By Newton's method, the second approximation can be derived from the first using the equation.
Since
,
and
Use these to find the approximation:
Example Question #467 : Derivative Review
Define
.Give the minimum value of
on the set of all real numbers.
The function has no miminum value.
This function is continuous and differentiable everywhere. First we find the value(s) of
for which .
Therefore, this is the only possible minimum. We determine whether it is a minimum by evaluating
:
Since
, has its minimum value at ; it is.
Example Question #1592 : Calculus Ii
Consider the equation
.
Which of the following is equal to
?
Example Question #1593 : Calculus Ii
Define
.Give the minimum value of
on the interval .
We first look for
such that :
The two values on the interval
for which this holds true are , so we evaluate for the values :
The minimum value is .
Example Question #1594 : Calculus Ii
Consider the equation
.
Which of the following is equal to
?
Example Question #471 : Derivative Review
Define
.Give the maximum value of
on the interval .
First, we determine if there are any points at which
.
The only point on the interval on which this is true is
.We test this point as well as the two endpoints,
and , by evaluating for each of these values.
Therefore,
assumes its maximum on this interval at the point , and .Example Question #1591 : Calculus Ii
Consider the equation
.
Which of the following is equal to
?
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