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 two different ways, use Mathematica  commands to determine which is larger: (100^99) or (99^100).

Problem 2

Evaluate (Sqrt[(2/((3^3)-1))+5*((4^2)-(2^3))]) 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) = (x^4)+3(x^3)-6(x^2)+2x-1, and g(x) = -2(x^4)+5(x^3)-11(x^2)+6x+1.

Part 1

Find ALL the values of x for which f(x) = g(x). Note there will be 4 solutions.

Part 2

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

Problem 4

Using the same functions f(x) and g(x) that were given in problem 3, determine the values of x for which f(x) > g(x).  Express your answer in interval notation!

Problem 5

Once, we will be using the same functions f(x) and g(x) that were given in problem 3.

Part 1

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.

Part 2

Create a graph which shades the region between  f(x) and g(x) for 0 ≤ x ≤ 0.5, make the color of the shaded region light red.

Part 3

Show both of the graphs from part 1 and part 2 on the same graph

Part 4

Add a plot the two intersection points of  f(x) and g(x) to the graph from Part 3 to produce a new graph which contains both functions, the shaded region, 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!

Problem 6

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 entry {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 {9, {10}} an element of FunList?  Use a Mathematica command to determine this!