Practice Problems
Problem No. 1
Assign the name w to the number
and then find the
exact value
and a
decimal approximation
for the following:
and
.
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Problem No. 2
Factor
.
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Problem No. 3
Enter the function
Then find the approximate value of
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Problem No. 4
Find the approximate value of T in the formula
when a=4.6 , b= -3.8 and c=2.9
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Problem No. 5
If
, find and simplify ,
.
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Problem No. 6
When multiplied out the expression
equals a fifth-degree polynomial.
What is the coefficient of the
term ?
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Problem No. 7
Plot the expressions
and
on the interval
![[0, 2*Pi]](/view.aspx?SI=1515/practice14.gif)
. Then plot these same expressions on the interval
![[0, 4*Pi]](/view.aspx?SI=1515/practice15.gif)
.
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Problem No. 8
Plot the function
on the interval
![[0, 2*Pi]](/view.aspx?SI=1515/practice17.gif)
. Automatic scaling does not produce a
useful picture. Specify a y-range that gives a good view of this
function on this interval.
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Problem No. 9
Recall that if a
rational number
has an infinite decimal expansion then
somewhere in the expansion the digits must repeat. A familiar example
is the decimal expansion of the fraction
= .33333... where we have the digit 3 repeated. A bit more interesting is the decimal expansion for
= 2.3571428571428... with the repeating digits 571428. Now look at a decimal expansion of the fraction
. Can you identify the repeating sequence. Check yourself by looking at one thousand decimal places.
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Problem No. 10
a) Plot the following points on a graph:
( 1, 0.53) , (1.5, 0.65) , (2, 0.91) , (2.5 , 0.95) and (3, 1.10 )
b) Create a single picture that has the points above
plus
graphs of the functions :
and
.
Use your picture to decide which of these two functions most closely fits this set of points ?
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Problem No. 11
Approximate all real solutions of the equation
.
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Problem No. 12
Approximate all real solutions of the equation
.
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Problem No. 13
The graphs of
and
intersect at one point.
Use the numerical solving capabilities of Maple to approximate the coordinates of this intersection point.
Start by entering an appropriate equation to solve.
Check your answer by creating a picture that shows the graphs intersecting.
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Problem No. 14
Solve for r in the equation :
. Be sure that you have entered the equation correctly. In particular check that you have used an * for
every
mulitplication.
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