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# Math 445 exam 1 example questions

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.