24/26- use algebra to find the limit exactly.

32- find k so that the function is continues or any interval

46- use a graph to estimate the limit. Use radians unless degrees are indicated by .

***PLEASE SHOW ALL WORK***

1. a. Using Figure 1.109, find all values of x for which fis not continuous. > Answer Answer > Solution -3 -2-1 1 2 3 + x Figure 1.109 of (x) X 6 Figure 1.110Figure 1.110 2. a. Using Figure 1.110, find all values of x for which fis not continuous. b. List the largest open intervals on which fis continuous. 3. Use the graph of f(x) in Figure 1.111 to give approximate values for the following limits (if they exist). If the limit does not exist, say so. a. lim f(x) I-+-3 > Answer b. lim f(x) I-+-2 > Answer c. lim f(z) > Answer d. lim f(x) > Answer e. lim f (a) > Answer f. lim f (x) C +3 > Answer of (x) -4-3-2-In Exercises 4-5, the graph of y = f(x) is given. a. Give the x-values where f(x) is not continuous. b. Does the limit of f(x) exist at each x-value where f(x) is not continuous? If so, give the value of the limit. X 1 2 3/4 f(x) 4. Figure 1.1126. Assume f(x) is continuous on an interval around x = 0, except possibly atx = 0. What does the table of values suggest as the value of lim f(x)? Does the limit definitely have this value? X -0.1 2-+0 -0.01 (x) 0.01 1.987 0.1 1.999 1.999 1.987In Exercises 8-9, a. Make a table of values of f(x] for x = -0.1, -0.01, 0.01, and 0.1. b. Use the table to estimate lim f (x). T-+0 sin(5x) 8. f(x) =\fIn Exercises 11-16, is the function continuous on the interval 1 11. on [-1, 1] T - 2 > Answer 1 12. on [0, 3] T - 2\fT. - 4x + 3 26. limsin (5x) Make sure your calculator is in radian mode and then use your calculator to estimate lim 2x (make a graph and/or plug in appropriate numbers to help you). O a. sin(5x) lim does not exist (DNE) 2x O b. sin (5x) lim NOT 2x O C. sin (5x) lim = 2 2x O d. sin (5x) im = 5 2xFind the value of k so that the function shown below is continuous on any interval: kx if0