The exam will have around ten questions, some easy, some not so easy. For most questions, you will be asked to answer with Matlab code in correct syntax. E.g.

Problem 1: (totally straightforward) Given a matrix , write one line of Matlab code that would assign the 3rd row of into the variable .

Problem 2: (slightly tricky) Given a matrix , write one line of Matlab code that convert the th column of into a row vector and assign it to the variable .

Problem 3: (pretty straightforward) Given a vector , write one or two lines of Matlab code that would return all the odd-numbered elements of . (By “odd-numbered elements”, I mean the elements with odd indices, e.g. .)

Problem 4: (moderate) Write Matlab code that defines a function named mysin that computes using the truncated power series

Note: an earlier version of this problem had an error in the Taylor series of .

Problem 5: (straightforward) Write Matlab code that would solve the system of equations.

Problem 6: (straightforward) Write a Matlab function that computes the mean (i.e. average) of the components of a vector according to the formula

where is the length of the vector. Your function should evaluate this sum directly using a for loop, not by calling Matlab's sum or mean function. You did this for lab, now see if you can do it without looking at notes.

Problem 7: (straightforward) Write a few lines of Matlab code that would plot versus on the interval using a red dashed line. Label the axes.

Problem 8: (a little harder than 7) Write a few lines of Matlab code that would plot on the interval , using the plotting function that would best highlight the functional relation between and . Label the axes.

Problem 9: Deduce the functional relationship from this graph.