from the left at 2 20. f(x) = if x * 1 a = 1 if x = 1 9. The toll T charged for driving on a certain stretch of a toll road is $5 except during rush hours (between 7 AM and cos x if x 0 sured in hours past midnight. (b) Discuss the discontinuities of this function and their 2x2 - 5x - 3 significance to someone who uses the road. 22. f(x) = if x * 3 x a = 3 10. Explain why each function is continuous or discontinuous. if x = 3 (a) The temperature at a specific location as a function of time 23-24 How would you "remove the discontinuity" of f? (b) The temperature at a specific time as a function of the In other words, how would you define f(2) in order to make distance due west from New York City f continuous at 2? (c) The altitude above sea level as a function of the dis- tance due west from New York City 23. f(x) = x - x - 2 24. f(x) = _ x - 8 (d) The cost of a taxi ride as a function of the distance x 2 - 4 traveled (e) The current in the circuit for the lights in a room as a 25-32 Explain, using Theorems 4, 5, 7, and 9, why the function function of time is continuous at every number in its domain. State the domain. 11-14 Use the definition of continuity and the properties 25. F(x) = 2x2 - x - 1 x2 + 1 of limits to show that the function is continuous at the given x 2 + 1 26. G(x) = 2x2 - x - 1 number a. 28. h(x) = sin x 11. f(x) = (x + 2x3)+, a = -1 27. Q(x) = Vx - 2 x3 - x + 1 12. g(1) = 12 + 51 30. B(x) = tan x 2t + 1 ' a = 2 29. h(x) = cos(1 - x2) 4 - x2 13. p(v) = 2302 + 1, a =1 31. M(x) = 1 + 32. F(x) = sin(cos(sin x)) 14. f(x) = 3x4 - 5x + Vx2 +4, a=2 15-16 Use the definition of continuity and the properties of 33-34 Locate the discontinuities of the function and illustrate limits to show that the function is continuous on the given by graphing interval 33. y = 34. y = tan Vx 15. f (x) = x + Vx - 4 , [4, 00) 1 + sin x 16. g(x) = x - 1 3x + 6' ( - 00 , - 2 ) 35-38 Use continuity to evaluate the limit. 35. lim x V20 - x2 36. lim sin(x + sin x) 17-22 Explain why the function is discontinuous at the given 37. lim x tan x 38. lim x3/ Vx2 + x - 2 number a. Sketch the graph of the function. 17. f(x) = - a =-2 x + 2 39-40 Show that f is continuous on (-0o, co). 18. f (x) = x+ 2 if x * -2 39. f(x) = =x ifxs1 a =-2 x - 1 if x > 1 if x = -2 40. f(x) = sin x if x TT /4 if x = 1 0 =1