2. Let g be the function whose graph is shown below. 3 2 1 y = } -1 -1 (a) Evaluate lim g(x), lim g(æ), and lim g(æ). 21- 22+ (b) Determine the asymptotes of the graph of g.
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- 14 Find the slope of the function ƒ(x) = -x - 1, by the definition of a limit. Slope =True or False: If lim f(x) = infinity as x-->2, then the graph of f has a horizontal asymptote at x=2.se the table feature of a graphing calculator to predict the limit. Check your work by using either a graphical or an algebraic approach. (If you need to use or –, enter INFINITY or –INFINITY, respectively.) lim x→6 f(x), where f(x) = 2 + x − x2 if x ≤ 6 13 − 9x if x > 6
- Draw a graph where limx→2f(x) exists but f(x) is discontinuous at x = 2. Name the type of discontinuitythat has this propertyLet G(x) = (x + 6)/(x2 + 4x - 12). a. Make a table of the values of G at x = -5.9, -5.99, -5.999, and so on. Then estimate limx--> -6 G(x). What estimate do you arrive at if you evaluate G at x = -6.1, -6.01, -6.001, .....instead? b. Support your conclusions in part (a) by graphing G and using Zoom and Trace to estimate y-values on the graph as x --> -6Suppose that ƒ is an odd function of x. Does knowing that lim x-->0+ ƒ(x) = 3 tell you anything about lim x-->0- f(x)? give reasons for your answer
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