Design a script file which solves each of the following problems in a separate cell. Please take the time to answer any questions that may be asked in the form of a comment in the appropriate cell. Graph the function 2y'--3x' + 5x,-2.5 x s 2.5 using first explod and then plot(). Find all the points of intersection between the functions (x)- xand g(x)-3". Use solveD and fzero) as necessary. Graph both functions on the same figure and visually confirm your answerS Compute each of the following: 1. 2. 3. b. lim d sin x deL x C. t. d (Aso compute the numerical value) 4. Find the following limit. In(1-x)+x lim Then use MATLAB to find the Power Series expansion (Google the command) of In(1-x) about x = 0 and explain how you can use this to take the limit by hand. Does it agree with MATLAB's limit? 5. Consider the function f(e)--2r+3+2t on the interval [-3/2,5/2). Graph the function on the given interval. Determine how many local extrema the function has. In particular, produce another graph which is zoomed in closer to x =-1 to confirm your result using the axis0 command Use MATLAB to differentiate f(1)and identify the critical points using fzero).You should also produce a graph to help you determine the "guess" value to use with fzero() a. b. c. d. Graph fO) on the interval -1.2si5-0.8. How does the graph establish that -I is in fact an inflection point of f()