Solve these problems. 8-22 even, 32, 36, 38, 42, 50-56 even and 66.

84 Chapter 1 Limits and Their Properties Continuity on a Closed Interval In Exercises 39-42, 2, x5 -1 discuss the continuity of the function on the closed interval. 73. f(x) = ax + b , - 1 4 2x - 5, x54 55. f(x) = - x+ 2 56. f(x) = x+ 2 x2 - 3x - 10 x2 - x - 6 cos x - 1 84. f(x) = x 1 64. Ax) = -2x + 3, x 2 66. f(x) = J-2x, x 5 2 (x2 - 4x + 1, x > 2 91. 50 - 1 x* 1 92 . f(x ) = [ 2x - 4, x # 3 x = 1 x = 3 tan 67. f(x) = |x| 2 93. f(x) = x4 - x3 +4 [1, 2] Making a Function Continuous In Exercises 69-74, find 94. f(x) = x3 + 5x - 3 [0, 1] the constant a, or the constants a and b, such that the function 95. f(x) = x2 - 2 - cos x [O, 77 ] is continuous on the entire real number line. 96. f(x) = -2 + tan TX [1, 4] 69. f(x) = 35, x21 70. f(x) = 3x, xs1 lax - 4, x 1 Existence of Multiple Zeros In Exercises 97 and 98, 4 sin x 71. f(x) = $. x5 2 explain why the function has at least two zeros in the interval , x> 2 72. 8 (x) = x 3 (4, 3) -NWA -2 32. lim f(x), where f(x) = [x2 - 4x +6, x 1 xSI C=-3 (-3, 4) (-3, 3) NWAW Continuity of a Function In Exercises 35-38, discuss the 3. 1 continuity of the function. 35. f(x) = = 12 - 4 36. f(x) = X - 1 (3,0) 3-2 -1 x + 1 c = 3 9. 10. (2. 3) 2- C= -1 1/ C=2 3 - - 3 - 2 - 1 1 2 D 2 -1- 12 3 4 5 6 (-1, 2) - 2- -2- 12 -3- -3- -3 (-1,0) Finding a Limit In Exercises 11-34, find the limit (if it 37. f(x) = [x] + x 38. f(x) = exists). If it does not exist, explain why. 11. lim - x8* x + 8 12. lim 13 x+ 3 - NW *- 5 13. lim 4 -X 1 5+ x2 - 25 14. lim * $4+ x2 - 16 15. lim x2 - 2r + 1 16. lim x+3 -3-2-1/ 212 3 - 3-2 1 2 x - 1 x--3* x2 + 7x + 12 -2+ -3 Copyright 2023 Cenga