LIM AP CALCULUS AB AVON HIGH SCHOOL MR. RECORD 2 Topic: 1.9 Connecting Multiple Representations of Day: 7 Limits Answer each of the following problems in this Four Corner Activity. f(x) = x2 - 3x -28 g (x) = x+4 h(x) = -2/x+41 y = f (x) Use the functions above to evaluate the following limits. If a limit does not exist, write dne. f (x) 1. lim x--4g(x) The graph of f (x), shown above, has a vertical asymptote at x = 6. Use the graph to evaluate the g (x) following limits. If a limit does not exist, write dne. 2. lim X-7 f (x) 1. lim f (x) 2. lim f (x) 3. lim_f(x) 4. lim f (x) x--1 x-6' 3. lim g(x) x- -4+ h(x) Topic: Limits Sketch a graph that meets the following guidelines 1. Which limit from the upper right corner does not 1. lim g(x) = 2, lim g(x) = -1, g(1) = 0 exist for the same reason as problem 2 on the upper left corner? 2. Sketch a graph of the limit described in the first problem from the top left corner. 2. lim h(x) = -0o, lim h(x) = too x -2 - x-2 lim h(x) = 2, lim h(x) = -2 X - -00 x-+00 3. Using problem 1 from the bottom left corner, 5 Ah ( x ) explain the difference between finding g(1) and lim g (x). 15LIM AP CALCULUS AB AVON HIGH SCHOOL MR. RECORD Topics: 1.10, 1.11 Day: 8 3 Exploring Types of Discontinuities Defining Continuity at a Point 1 Topics: 1.12, 1.13 Confirming Continuity on an Interval Removing Discontinuities Learning Objective LIM-2.A: Justify conclusions about continuity at a point using the definition. Learning Objective LIM-2.B: Determine intervals over which a function is continuous. Learning Objective LIM-2.C: Determine values of x or solve for parameters that make discontinuous functions continuous, if possible. Eroded pedestrian bridge in Southeast Collapsed Hwy US 36 north of Denver, CO, Bahia Honda Rail Bridge, Lower Keys Florida. Texas from Hurricane Harvey, Fall Summer 2019 2017 TIP: Continuity implies "no interruptions" in the graph. Three Examples of Discontinuities of a Function 3 Criteria of Continuity over an interval (a, b) In order for a function, f(x) 1. f(c) is undefined 2a. lim f (x) does not exist 3. lim f (x) * f(c) to be continuous at a point, x ->C x = c, the following three conditions must be met. 1 . 2. b or 2b. OFRO 3 . Scan the code above to b watch a video on the Introduction to Continuity 16