Important When answering questions in a mathematics course always be sure to use the following guidelines to help you do your best: . Provide full solutions, showing all of your steps. . Make sure that there is one step or idea per line. . Use one equal sign per line. . Make sure that equal signs line up vertically. . Don't use self-developed short form notations. 1. Determine the following limits (if they exist). (2 marks each) a. lim (3x4 + 2x2 - 5) I +3 b. lim () c. lim x'+x-20 8-2x 2. Evaluate the following limits (if they exist). (3 marks each) a. lim b. lim Va+16-4 c. lim Va-4 x-64 3. From first principles (i.e. using the tangent slope method), find the slope of the following curves at the given value of c. (3 marks each) a. f (x) = 2x2 - 6x at x = 3 b. y = 3x +latx = -4 4. Look at the graph below of the derivative f (x). From this, make a sketch of the original function f () and of the second derivative f"(a), and explain your reasoning. (7 marks)