Solve

Please answer the following questions and explain your reasoning wherever necessary. Question 1: Verify that the function f(a) = x2 - 5 + 3 over the interval [-2, 2), satisfies the three criteria stated in Rolle's Theorem. If applicable, calculate the point c where f'(c) = 0. Question 2: Determine whether the function f (a) = _ satisfies the two conditions of Mean Value Theorem on the interval 1, 4). If it does, find all possible values of c such that f'(c) (4 - 1) = f(4) - f(1). Question 3: Consider the following limits: 2xsecr 1. lim (tanx re - log(1 + x) ll. lim 2:2 5 Ill. lim 1+ IV. lim log (1 + kx?) c-0 1 - cosx V. lim(x2 - 1 )tan( ?) a. Identify the indeterminate forms for each part (1-V) of question 3 above and provide a detailed demonstration. b. Evaluate each part (I-V) of question 3 above using L'Hopital's Rule and show the calculations at each step