Please answer the following:

(1 point} Let x} 2 $3 3:1: 1.5. Determine whether the lnterrnediate Value Theorem can be used to show that f(1:) has a root in the interval {0, 1). Answer: Since: positive, negative, continuous, discontinuous i)_f is ? K v on [0,1], ii) u) = ,and in) H1) 2 ' can/cannot the Intermediate Value Theorem ? med to show that x) has a root in the interval (0, 1). (1 point) Suppose f(a) = -2x2 + 3. Evaluate the following limit. f( -2 + h) - f(-2) lim h-0 h Note: Input DNE, infinity, -infinity for does not exist, oo, and -oo, respectively.('1 point} Suppose f(2?) = 8.1':2 + C, where C is any real number. Then the expression f(4 + h) H4) k can be written in the form Ah + 3(4), where A and B are constants. Find: 3 5$+4 ('1 point} Suppose f(2?) 2 .Then the expression 1% + h) t!) It can be written in the form Wm, where a, A, B, C, and D are constants. Find: (a) A = (b) B = (c) C = (d) D = x2 - 6, (1 point) Let f(a) = 2x - 7, r >C If f (ac ) is continuous everywhere, then c =x- 7 (1 point) Use interval notation to indicate where f (a ) = is continuous. (z - 5) (2 + 5) Answer: I E Note: Input U, infinity, and -infinity for union, oo, and -oo, respectively.1 (1 point) Use interval notation to indicate where f (a) = is continuous. 1 + el/x Answer: I E Note: Input U, infinity, and -infinity for union, oo, and -oo, respectively