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Practice Problems

Problem No. 1

Assign the name w to the number   2*Pi/3   and then find the exact value  and a decimal approximation  for the following: w^2, sqrt(w)  and cos(w)  .

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Problem No. 2

Factor    x^8-2*x^4+1  .

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Problem No. 3

Enter the function f(x) = 20*x+30*x^2-sqrt(46-x^2)  

Then find the approximate value of   f(3.29)+f(-3.1)

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Problem No. 4

Find the approximate value of  T in the formula    T = sqrt((2*a-3*b^2)/(c-20))  

when a=4.6  ,  b= -3.8  and c=2.9

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Problem No. 5

If   f(x) = x^2-2*x+3  ,  find and simplify ,    f(3*t+2)  .

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Problem No. 6

When multiplied out the expression    (x-4)^2*(x+1)^3   equals a fifth-degree polynomial.

What is the coefficient of the   x^2   term ?

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Problem No. 7

Plot the expressions   cos(x)  and   cos(x)*sin(10*x)  on the interval [0, 2*Pi]  . Then plot these same expressions on the interval [0, 4*Pi] .

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Problem No. 8

Plot the function    f(x) = sec(x)+4  on the interval [0, 2*Pi]  . 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 1/3  = .33333... where we have the digit 3 repeated.  A bit more interesting is the decimal expansion for   33/14  = 2.3571428571428... with the repeating digits 571428. Now look at a decimal expansion of the fraction   2/19 . 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 : f(x) = sin(x/2)  and   g(x) = x^2/5  .

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    x^4-4*x^3+3*x-12 = 0  .

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Problem No. 12

Approximate all real solutions of the equation    x^4-4*x^3 = cos(3*x)+3  .

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Problem No. 13

The graphs of    f(x) = 20-x   and    h(x) = 1.012^x   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 :   r*(p*k-18*m) = 32*(2-p*r*m)/(m^2)   . Be sure that you have entered the equation correctly. In particular check that you have used an * for every  mulitplication.

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