Please answer all questions and provide a brief explanation of the solution.

Question 1 7.7 pts My = sin (u), u= v - , andv = In (z) . then the value of $ atz = e is 0 1 Question 2 7.7 pts The average value of sec' z over the interval 0 S = S ; is Question 3 7.7 pts If x3 + 3zy + 2y' = 17, then in terms of z and y. = = o - ( ) o - ( ) o - () Question 4 7.7 pts Let be a polynomial function with degree greater than 2. If a * b and f(a) = f(b) = 1, according to Rolle's Theore value of z between a and b? Allowing must be true for at least one 1. f( z ) = 0 11. f'(2) =0 11. f" ( 2 ) =0 O I and II only O ll only O I only ( 1, 11, and Ill Question 5 7.7 pts The graph of / (z) = = is concave downward for all values of x such that Oxen Question 6 7.7 pts The absolute maximum value of f(z) = x3 - 3x3 + 12 on the interval [-2, 4] occurs at z = 02 01 0 2 Question 7 7.7 pts Find & for y = In v2 +4 o M Question 8 7.7 pts Find y given y " zsteff None of these Question 9 7.7 pts Find lime-too Inlay 01 Does not exist 02 Question 10 7.7 pts If f(z) is continuous at z = a , which of the following is not necessarily true? of' (a) exists O lims te f(2) = f(a) Of(a) is defined O lime-to f(z) exists Question 11 It f(z) = 2sin (#), then O -2sin (#) O - sin (#) O -8 sin () -+sin (4) Question 12 7.7 pts Let f(z) and g(z) be two functions whose values at a - 0, 1, and 2 are given in the table below. 2 1(2) 8 8 (2 ) 8 0 1 21 2 2 7 " H(z) = el(=) + wz. then H'(0) = Onte Oe Question 13 7.6 pts Let f(z) and g(z) be two functions whose values at a = 0, 1, and 2 are given in the table below. 2 1(2) 5 8 (2) 8 0 1 -1 2 1 1 2 4 0 2 7 3 11 05 02 O 04