Consider the graph of the function f(x). Determine the following limits or state why they do not exist. a. b. C. d. lim f(x) = f. x4-2- lim f(x) = 24-2 lim f(x) = lim f(x) = e. lim f(x) = X-00 lim f(x) = 2118 4. An infinite limit is when 5. A limit at infinity is when 49 3. T -5 " P 2 0 2 Fer 3 -on and graphically give us and graphically gives us 6 7 8 X 6. Sketch a function with given properties. lim f(x)=-4 lim f(x) = x+1+ lim f(x) = 0+x f(0) =-2 lim f(x) = x+1+ 00+x lim f(x) = x-1 -4 -3 -2 lim_ f(x)= x-2 -1 lim f(x) = x-1- y 4 3 a. Use the graph to find the following values or state that they do not exist (write DNE). 2 1 -1 -2 -3 7. DEFINITION: Limit of a Function: Suppose the function f is defined for all x near a except possibly at a. If f(x) is arbitrarily close to L (as close to L as we like) for all x sufficiently close (but not equal) to a, we write lim f(x) = L and say the limit of f(x) as x approaches a equals L. xa -4 lim f(x) = 2 X4-8 2 3 4 y 71 lim f(x) = -00 x-1- 6 5+ 4 3 2+ f(x) 14 W -X -4-3-2 -1 0 1 2 3 4 5 -1- -2- -3-