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5-6 The graph of a function f is given. (a) At what numbers a does lim x-a f(x) not exist? (b) At what numbers a is f not continuous? (c) At what numbers a does lim x-a f(x) exist but f is not continuous at a ? 5. YA 6. YA O- + X(d) The cost traveled (e) The current in the circuit for the lights in a room as a function of time 13-16 Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a. 13. f(x) = 3x2 + (x + 2), a = -1 +2 + 5t 14. g(t) = 2t+ 1 " a = 2 15. p(v) = 2/302 + 1, a = 1 16. f(r) = $/4r2 - 2r+ 7, a=-2 17-18 Use the definition of continuity and the properties of limits to show that the function is continuous on the given interval. 17. f(x) = x + Vx - 4, [4, 00) 18. g(x) : x - 1 3x + 6' (- 00, - 2) 19-24 Explain why the function is discontinuous at the given number a. Sketch the graph of the function. 19. f ( x ) = x + 2 a =-2 20. f( x) = * + 2 if x * -2 a =-2 if x = -255-58 Use the Intermediate Value Theorem to show that there is a solution of the given equation in the specified interval. 55. -x' + 4x + 1 = 0, (-1, 0) 56. In x = x - Vx, (2, 3) 57. ex = 3 - 2x, (0, 1) 58. sin x = x2 - x, (1, 2)