The graph of the function fis shown. 0 - -2 -4 -6 -10 -8 -6 -4 -2 2 4 For what values of c does lim f(x) = 2? X-c O-6 only O -4 only O -6 and -4 O -6, -4, and -2The graph of the function h is shown. Why is _lim 117(1} nonexistent? O The limit is unbounded. O The limit from the left does not equal the limit from the right. O The limit is oscillating around the xvalue. O The xvalue is approaching the endpoint of an interval. \fThe size of a balloon is changing with respect to time, such that the volume is given by V(t), where V(t) is measured in cubic centimeters and t is measured in seconds. A tangent line is shown for V(t) at t = 2 seconds. Determine the best estimate for the value of the instantaneous rate of change of V(t) when t = 2. V(t) y 6 -21 2 3 5 6 7 S O V(2)-V(1) O V(lim t) 1-1 O AV(t) 2 O V(2.01)-V(1.99) 0.02The graph of the function g is shown. 3 2.5 2 1.5 0.5 0 - 0.5 -1 -1.5 -23 -2 -1 2 3 5 6 What is lim g(x)? x-+2 O DNE O-1 OO 01Values of f{x) at selected values of x are shown in the table. x |275 (29 (299 |301 |31 (325 fix) | -3.313 | -3.05| -3.001| 4.000 | 4.05 [ 4.313 Based on the data in the table, apply what you have learned about one-sided Iimits to determine if J!i"":"'("'f) exists. If it does exist, determine what it equals, and If it doesn't exist, explain why. The graph of fis shown on the coordinate plane. Selected values for g are shown in the table. Graph of f UJ -1 -6 -4 -2 x-values -2 0 6 g(x) values 1 4 3 2 Limit values of g(x) lim g(x) =5 lim g(x) = 0 lim g(x) = 2 lim g(x) = -2 x- -2 X-+0 x-5 X-+6 a. Use the graph of f and the table of g to determine lim 27 ( x ) 2 - 3 according to limit theorems. (3 points) f(g(x)) b. Find lim f(*) or explain why it does not exist. Use correct limit notation in your answer. (3 points) c. If m(x) = x2 - 2x and n(x) = Vx- 1-1 find limm(x)n(x). Justify your answer and use correct limit notation in your work. (4 points) X-+2