mathematica

 

1.Let f(x)=x^4-5x^3-7x^2+x-6 and  g(x)=x^3-12x-5.  Plot  f(x) and  g(x) on the same graph, with f(x) in red and g(x) in blue.  Use an appropriate domain and range that show all key features (intercepts, maximums, minimums, intersections) of the two functions.  Label the axes appropriately. Use specialized ticks, not the defaults given by Mathematica
2. Use Solve commands to find the location (the x-value is sufficient) of all intersections of f(x) and  g(x) in Problem 1.
3.Use Solve commands to find the location of all x-intercepts of each function from Problem 1.
4.For what value(s) of a (if any) is the graph of f(x)=a x-4 tangent to the graph of g(x)=-(2/a) x^2?  Work this problem in two ways:  1) use the Manipulate command and a plot to estimate the value(s), 2) algebraically determine the exact value(s).

Problem Set 1
NAME:

Directions: Do the following problems using Mathematica. Show your work,

record your answer, and offer an explanation (if required) as appropriate. Save

your completed work and post your assignment to Blackboard no later than

11:59p on Friday, August 28.

Problem 1
There is at least one error in each of the following three Mathematica com-

mands. Describe the error(s), correct the error(s) with a revised command, and

run the revised command to ensure it works properly.

In[ ]:= Rationalizⅇ[.532]

(*Show work here*)

In[ ]:= SineArcCosine5  13

(*Show work here*)

In[ ]:= Solvex3 + 3 x – 19 = 0, x

(*Show work here*)

Problem 2
Compute 7

13
+ 21

18
– 40

3
exactly and also find a numerical approximation for the

exact answer.

(*Show work here*)

Problem 3
Find the exact value of the 58th digit to the right of the decimal point in the num-

ber 3 ⅇ2 π + 2. Note that ⅇ is the number “e.”

(*Show work here*)

Printed by Wolfram Mathematica Student Edition

Problem 4
Compute 8

x2-4 x+3
– 3

x2-x-6
as a single fraction with the denominator in factored

form.

(*Show work here*)

Problem 5
Let f(x) = x4 – 5 x3 – 7 x2 + x – 6 and g(x) = x3 – 12 x – 5. Plot f(x) and g(x) on the

same graph, with f(x) in red and g(x) in blue. Use an appropriate domain and

range that show all key features (intercepts, maximums, minimums, intersec-

tions) of the two functions. Label the axes appropriately. Use specialized ticks,

not the defaults given by Mathematica.

(*Show work here*)

Problem 6
Use Solve commands to find the location (the x-value is sufficient) of all intersec-

tions of f(x) and g(x) in

Problem 5.

(*Show work here*)

Problem 7
Use Solve commands to find the location of all x-intercepts of each function from

Problem 5.
(*Show work here*)

Directions for Problems 8 & 9
Solve each of the following equations as completely as possible. If exact solu-

tions can be presented by Mathematica, present those solutions as well as

approximate numerical values for the solutions. If exact solutions cannot be

presented by Mathematica, find approximate numerical solutions. In all cases,

verify each solution in two ways: 1) by plotting appropriate functions over appro-

priate intervals, and 2) by using a replacement operation.

2 Problem Set 1 F20 (3).nb

Printed by Wolfram Mathematica Student Edition

Problem 8
x2

4
= -3 + x4 – 8 x2 + 16

(*Show work here*)

Problem 9
2x+3 = 8 x2 – 3 x + 5

(*Show work here*)

Problem 10
For what value(s) of a (if any) is the graph of f(x) = a x – 4 tangent to the graph of

g(x) = – 2
a

x2? Work this problem in two ways: 1) use the Manipulate command

and a plot to estimate the value(s), 2) algebraically determine the exact value(s).

(*Show work here*)

Problem Set 1 F20 (3).nb 3

Printed by Wolfram Mathematica Student Edition