This unit is continuity for calculus. Please explain how to solve each question.

question 17 19 20 39 40 45

4. From the graph of 9, state the intervals on which g is 39. For what value of the constant c is the function f continuous continuous. on (-0o, 00) ? [-4-2) ( 6 , 8 ) f ( x ) = cx + 1 if x = 3 (cx 2 - 1 if x > 3 40. Find the constant c that makes g continuous on (-co, co). g ( x ) = x2 - c? if x 4 41. Which of the following functions f has a removable disconti- ( - 2 , 2) 1 [2, 4 ) nuity at a? If the discontinuity is removable, find a function g (4 , 6 ) that agrees with f for x * a and is continuous on R. 9. If f and g are continuous functions with f(3) = 5 and (a) f(x) = * - 2x - 8 a = -2 lim:-3 [2f(x) - g(x)] = 4, find g(3), *+ 2 fly, are continues fig ) =5 sis ( b ) f ( x ) = * - 7 x - 71' a = 7 15-20 I'll Explain why the function is discontinuous at the given number a. Sketch the graph of the function. (c) f ( x ) = - * + 64 *+4 ' a = -4 17. f ( x ) = 1 - x2 if x 1 9 - x x' - x -.12 45-48 1Ill Use the Intermediate Value Theorem to show that there is 19: f(x ) = if x = -3 x+ 3 a =-3 a root of the given equation in the specified interval. -5 if x = -3 45. x* + x - 3 = 0, (1, 2) 46. Vx = 1 - x, (0, 1) 20. f ( x ) = 1 + x 2 if x