1. You are testing a theory which says that the output displacement of a measurement device should vary with time according to the equation:

D(x) = {x² cos (x)} / (x +1)

So far, you have measured the following set of experimental data for D and t:

1) Plot the function ( ) in the range of . Use increment of 0.1.
2) On the same plot, aslo plot the above Data (M versus t).
3) Add a title, label the axes, and use proper legends appropriately. Submit the graph and the m file (both copied in your word file) you have produced to produce the plot.

2. Write a MATLAB function that can be used to solve a quadratic equation if answers are real numbers (you have to do following steps):

2ax² - 3bx + 4c = 0

. The inputs to the function are the three coefficients a, b, and c.

. Check if the equation has real solutions. If there is no real solution the program should display ‘THERE ARE NO REAL SOLUTIONS' then quit the program.

. Otherwise, calculate the solutions and display them as shown in the following example (use the fprintf command showing each solution with

4 decimal points). As example:

‘The solutions are -3.4135 and 9.7435'

.Try to solve two quadratic equations with coefficients: [a, b, c] = [1 , 1, -4] and [a,b, c] = [5 -1 3]

Submit the m file for your function, and the results of both test runs done in MATLAB (again copy and paste them in the word file)

3. a) Write a function m-file that will calculate the function f(x)

f(x) = e^-x

b) Calculate f(1) in MATLAB and print it in with 15 decimals.

c) The taylor series for the function f(x) is given as

f(x) = e^x = 1 - x + x² / 2 -x³ / 6 + x⁴ / 24 + ... + (-1)n xⁿ / n! + ...

If we only take 6 terms (including constant term) of this series to compute f(1), what is the true percentage error? Use answer in part (b) as true answer.

4. Answer the following questions (keep your answers short and precise)

a) Explain the differences of operators ‘ * ' and ‘ .* ' in MATLAB.

b) The following MATLAB script is written in MATLAB by another user but when you try to use it function value generate error message. Please correct these statements so it will generate y(x) on the domain, x from 0 to 2π.

Y(x) = {e^x cos² (x)} / (x³ + 3x)

The MATLAB script

x = linspace(0,2pi);

y(x)= e^x*cos²(x)/x³+3x

5. Develop a MATLAB function that will compute the following function. Test your function for t = 7, 15, 25 and 100. Include your m file and the output of your tests in the word file.

Plot the function in the range of -4 ≤ t ≤ 6