AP Calculus BC Module 1 DBA Be sure to show and explain all work. Use concepts learned in this module to complete this problem set: determine limits algebraically, using graphs, and considering tables of data values; apply conditions of continuity, use of the Intermediate Value Theorem. 1. Determine each limit using the method indicated: a. Using a table: lim,- 9 points b. Algebraically: lim, -8 3-84 VX+1-1 lim c. Algebraically: 2. Non-calculator: Sketch the graph of fix) and identify any values of c for which lim, , /(x) does not exist. Explain. (x -8 - 21 8 points 124 3. Evaluate the difference quotient, lima, 2, for fix) = 3x + 7x + 5. 8 points4. Non-calculator: Find a nonzero value for the constant & that makes /(x/ continuous at x = 0: 8 points tankx ( x) - for 3x + 2k X20 5. Non-calculator: Consider a circle with a radius of k. Explain and show why there must be a square that has a diagonal with a length between k and 2k and an area that is half the area of the circle. B points 6. Use your graphing calculator to graph / (x) = x + . Sketch its graph on your paper. 9 points a. At what point, c. is there a point of discontinuity? What kind of discontinuity? Why? b. Use a table to determine the limit of fix) as x approaches c (the 'c' that you determined in part i). What is the limit as x - c ? Provide a table of values that you have used to answer this. c. Now show analytically that the limit as x approaches c is that which you found in part