Find the constant a such that the function is continuous on the entire real line. 7sin x X a = g(x) = a 3x if x < 0 if x 0 Describe the interval(s) on which the function is continuous. (Enter your answer using interval notation.) f(x) = xx + 5 Verify that the Intermediate Value Theorem applies to the indicated interval and find the value of c guaranteed by the theorem. x + 6x + 1, [0, 7], f(c) = 17 C = f(x) = Verify that the Intermediate Value Theorem applies to the indicated interval and find the value of c guaranteed by the theorem. x + x C = f(x) = x - 1 1 5 4 f(c) = 6 Find the limit (if it exists). (If an answer does not exist, enter DNE.) x - 2x + 3 -x+2x+1 lim (a), where (x) = { f if x < 1 if x 1 Consider the following. f (x) X- 4 r2 +5r 36 Find the x-values at which fis not continuous. Which of the discontinuities are removable? (Enter your answers from smallest to largest. Enter NONE in any unused answer blanks.) X = X = = ; ---Select--- ---Select---