Question 1: Consider the following function f (x) = sqrt(125-x^3), 0 x

(a)

Construct a half-range expansion of f , assuming that f is extended to the interval [?5, 0] as an odd function. The definite integrals appearing in the series should be evaluated numerically using the function trapz. For this purpose the interval [0, 5] can be discretized using 200 subintervals. On one graph, plot the function f on the interval [0, 5] using a red line of thickness 3, the extension of f on the interval [?5, 0] using a blue line of thickness 3, and the series truncated after 1, 2, ... , 7 terms (i.e., there should be 7 curves, each corresponding to the series with a different number of terms) on the interval [?10, 10] using a black line of thickness 1. Use your First Name, Last Name, and Student Number as the title for the graph (e.g., 'Johnny Good, 1234567'). Then save the graph as a Portable Network Graphics (.png) file, and upload it.

(b)	Repeat part (a) above, but this time assume that f is extended to the interval [?5, 0] as an even function.

(c)

Repeat part (a) above, but this time assume that f is extended to the interval [?5, 0] through an identity reflection, i.e., as f (x) = f (x + 5). I need help with graphing all parts of question 1 using MATLAB. Note: I will not be able to check if my answer is correct until after the deadline so please only submit an answer if you are confident in it.