Math 1205 - Worksheet 1 Problems

Instructions:

  • Create a Word document. Number each problem clearly.
  • Use Matlab-generated graphs and tables imported into the document. If you are using Word 98 on the Emporium computers, you should choose the Paste Special option and make sure that “float over text” is NOT checked.
  • Show both the correct input and corresponding output for each problem. Do not copy any incorrect or extraneous commands into your Word file.
  • Refer to “Getting Started” and “Matlab Basics” for help with Matlab.

Problems:

  1. Have Matlab compute the following arithmetic problems:
  1. (2 + 43) multiplied by 3
  2. In each of (i)-(iii) first predict the answer, then use Matlab to calculate the answer, and finally, describe in words the order of the operations.

(i) 16/4^2/4

(ii) (16/4)^2/4

(iii) (16/4)^(2/4)

  1. (i) Define an array x to be the first 3 multiples of 4 ( 4, 8, 12).

(ii) Define an array y to be 1, 7, 22.

(iii) Perform an array operation that multiplies each element in x by the corresponding element in y. (iv) Perform an array operation that divides each element in x by the corresponding element in y.

(v) Make a table with a column for x and a column for y.

  1. Let and .

a. Create a table of values for the function over the interval [-2, 2] at steps of 0.1

Make a column for x and a column for .

b. Graph on the interval [-2, 2].

c. On your graph, insert the and axes; that is, plot the lines and .

d. For what values of does ? How can you tell from the graph? (Use the zoom command

to get numbers accurate to the nearest tenth.) How can you tell from the data?

  1. Define to be symbolic and redefine and . Then use the solve command to find the answers in part d more exactly. What problem do you encounter with the solve command in finding the solutions?
  2. Use the fzero command to find all of the answers in part d.

3. Use the fzero command to solve the equation using the variable “t”. Copy the resulting error

message into your Word file. Find the correction to this error in “Matlab Basics”. What must you do to

find the solution using fzero?

4. a. Graph the line through the points (1, 3) and (2, 6) in the window –2 ≤ x ≤ 4 and –8 ≤ y ≤ 8.

b. Plot the point on the same set of axes. Mark it with an 'x'.

c. Using your graph, does the point lie on the line?

  1. a. Graph over the interval [0, 2]. Place an “o” at intervals of 0.2 units. Copy your input and

the resulting graph into your Word file.

  1. Sketch the graph again, this time making the horizontal and vertical axes the same scale. Use Matlab’s built-in help (help axis) to find the necessary plot option. Copy the input and new graph into your Word file.