Math 1483 - Quiz 1

YOUR NAME HERE

Remember, ALT+7 gives a new text cell, be sure to explain your answers, if needed!

Problem 1

In at least two different ways, use Mathematica  commands to determine which is larger: (101.11^(-99.9999)) or (99.01^(-101.01)).

Problem 2

Evaluate (((((2+(7^3))/(56-4*(7-3)))))^(17+(4/3)))-((((12-3))^5)/(Sqrt[(13/521)])) in the following two ways:

Part 1

Simplify the expression given in the problem, keeping your answer exact.

Part 2

Numerically approximate the expression to 10 decimal places.

Problem 3

Let f(x) = 4(x^6)-3(x^5)+2(x^4)-7(x^3)+14(x^2)+18x+12, and g(x) = 10(x^6)-4(x^5)+2(x^4)-2(x^3)-72(x^2)+54x+52.

Part 1

Find ALL the values of x for which f(x) = g(x). Note there will be 6 solutions.

Part 2

Use the Solve command to find only the four real solutions to the equation f(x) = g(x).

Part 3

Determine the values of x for which f(x) > g(x).  Express your answer in interval notation! (Hint: The Reduce function is your friend)

Part 4

Plot the functions f(x) and g(x) on the same graph, where the graph of  f(x) is magenta in color, and g(x) is cyan in color.  Be sure to plot on a domain which contains all the points of intersection between the two functions.

Part 5

Add a plot of the two intersection points of  f(x) and g(x) to the graph from Part 4 to produce a new graph which contains both functions and now the two points of intersection.  Pick an icon from:

https://reference.wolfram.com/language/guide/ShapesIconsAndRelatedCharacters.html

which is NOT “▽”, and make sure that the points show up on the resulting graph!

Part 6

Create a graph which shades the region between  f(x) and g(x) for the two roots closest to the origin. Make the color of the shaded region light red.

Part 7

Add the plot from Part 6 to the plot from Part 5. I.e. your new plot should show two functions, 4 points of intersection,  and a shaded region.

Problem 4

Consider the following list: (Be sure to press shift+enter on the next line to store the list in the variable FunList).

FunList = {{},{1,2},{3,4,5},{{6},{7}},{{8,9},{10}},11,12,13}

Part 1

How many elements are there in FunList?

Part 2

If we needed to get at the value of {10} in FunList, what indexing command do we need to use?

Part 3

If we needed to get at the entry 10 in FunList, what indexing command do we need to use?

Part 4

Is {8, 9} an element of FunList?  Use a Mathematica command to determine this!