this is mty question. thank you !

Question 1 ( 6+ 5 + 7 +7 = 25 marks). You must show all your working to obtain marks for each question. (a) Consider the function f(I) = and the partition P = {0, 1, 2, 3}. (i) Use the Mean Value Theorem to show that there exists at least one point in the domain [0, 3] for which the derivative is -1/2. (ii) By taking the derivative of f(x), find the value of a where the derivative is -1/2. (b) (i) Is the expression I = r+1 12 + 4r + 1 d.r Riemann integrable? Say why or why not. (ii) By partitioning the interval [1, 5] into four parts and computing upper and lower sums, estimate the integral in part and report it to 4 decimal places (iii) Evaluate the integral exactly (analytic expression) and express this as a decimal to 4 places. (c) Use the e - 6 definition of limit to show that lim f(x) = 13 . 1-+2 for the function f(x) = 4x2 - 3. (d) Showing all working, use L'Hospitals to evaluate: lim 1- e 2 401 - cos