dont use AI

Problem #1: Consider the following function f(x) = (a) Construct a half-range expansion of f, assuming that f is extended to the interval [8, 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, S] can be discretized using 200 subintervals. On one graph, plot the function f on the interval [0, S] using a red line of thickness 3, the extension of f on the interval [ S, 0] using a blue line of thickness 3, and the series truncated after l, 2, , 7 terms (i.e., there should be 7 curves, each corresponding to the series with a different number of terms) on the interval [ 16, 16] using a black line of thickness l. 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 [ 8, 0] as an even function. (c) Repeat part (a) above, but this time assume that f is extended to the interval [ S, 0] tluough an identity reflection, i.e., as f(x) = + S).