5- 8: A11 Limits That Do Not Exist Example #1 Find each of the following from the graph. a) lim f(x)= b. lim f(x) = 0 x-2 c) A(2) = d) Does lim f(x) exist or not? Why or why not? -3 Example #2 Find each of the following from the graph. a) lim f(x) = b. lim f (x) = c) A(2 ) = d) Does lim f(x) exist or not? Why or why not? Example #3 Find each of the following from the graph. a) lim f(x) = b. lim f (x)= x -+ 2 - x -+ 2+ c) A(2) = d) Does lim f(x) exist or not? Why or why not? x-+ 2 - 34Based on what you have seen so far, does f(a) have to be defined in order for the lim f (x) to exist? Draw x -> a and explain two different graphs to justify your reasoning. In both graphs, f(a) should be undefined but in one graph, the limit should exist while in the second one, it should not exist. Below is a table of values of an exponential function. Use the table to find the limits that follow. X -9 -S 3 f ( x) $13 33 1.5 1.125 1.002 a) lim f(x) b) lim f(x) c) lim f(x) d) lim f(x) X-+1' Below is a table of values of a rational function. Use the table to find the limits that follow. - 1000 -1.001 0.999 0 1,999 2 2.001 1000 F(x) 1,002 2001 Undefined w 1999 0.333 Undefined | 0.334 0.998 a) lim f(x) b) lim f(x) c) lim f(x) d) lim f (x) e) lim f(x) f) lim f(x) x -+2 1- -1A Graphical Analysis of Limits Analysis of Limits Using the graph, find the value of each of the following limits. If a limit does not exist, state why. a) lim f(x) b) lim f(x) c) lim f(x) x-+3 x--5 c) lim f(x) x - 3 d) lim f(x) e) lim f(x) x -+2 x -+ 2+ f) lim f(x) g) lim f(x) h) lim f(x) X-+2 X-7-20 X - *0+ A Graphical Analysis of Limits Find the value of each of the following limits using the graph of g(x). If a limit does not exist, state why. a) lim g(x) b) lim g(x) c) lim g(x) x -+3 d) lim g(x) e) lim g(x) f) lim g(x) X-4 g) lim g(x) X-4 h) lim g(x) i) lim g(x)