The following four expressions are exactly equal to zero: 15000 11 = 15,001, 500 - 10,000 0.3k 0.0142 - 416,791,675 30,000,000 x3 = 13 = 15,000,000 - [ 0.5 15,000,000 - 30,000,000 0.1 - 3,000,000 14+ 0.1 – 3,000,000 since computers store floating-point numbers (numbers with decimals) with a finite storage space, most numbers are stored with a small truncation error (recall when we did sin() in class and found a number x10-16). usually this error is too small to worry about, but it accumulates if you add up the number multiple times. to verify this effect, use matlab to compute 21, 22, 23 and 24. you should compute the sums using a for loop. what do you get for 11, 12, 13 and 24? which of your errors is the largest? which of your answers is exactly zero and which is not? why do you think that might be the case? in particular you should discuss is and x, and give a reason as to why these numbers are so different (hint: think about the denominators of 0.1 and 0.5, if you write them as fractions). 2. the n-th order taylor-series approximation to cosine is given by costr) cos(r) = 2 (-1)" 2 (2k)! to plot cos(x) on the interval (- ), we first create a vector in matlab with many values in between - and , e. g., x = -pi: 0.01.pi. then, we use the plot command to plot e. g., plot (x, cos( create a plot of cosine on the interval -, and plot the taylor-series approxi- mations for n = 1, 2, 3, 7. each plot should be on the same axis in the same figure. in order to receive full credit, your plot must have the following features: (i) the line width of the lines is 2. (ii) the x-axis is labeled with the text "z-values". (iii) the y-axis is labeled with the text "cos(x)" (iv) there is a title with the text "cos(2) and its taylor approximations." (v) there must be a legend with 5 entries (one for each plot). the legend should be in a place that does not block the plots. (vi) the font on your axes and title should be large enough to read without zooming in: a font size of about 10 is good.