[1] Please state your answer as \"True\" or \"False\". (a) The derivative of the function f (:13) = tan(2.'1:2 + 59:) + 5 is f'(m) = sec2 (4:1: + 5). x3+27 (b) The fllIlCtIOIl f($) = m is continuous on (00, 00). (c) The limit lim 1 = 00. mrO :13 (d) The range of f(:z:) = arctana: is (00, 00). (e) The absolute maximum value of the function f (m) = sin(2:c) on [Zr, E] is 1. (f) The dimensions of a 6sided cardboard box made to hold 64 cm3 of sand using the least amount of cardboard is 40111 X 4cm x 4cm. [2) Please box your nal answer and show your work. (a) What is the domain of f (x) = sin(ln(5$ 1))? (b) Find the largest interval containing 1 on which f (x) 2 4mm is onetoone. (c) What is the inverse of the function from part (b) on the Specied interval? (d) What is the value of f: e5m2$dat? (e) If f is continuous and few f($)d$ = 10 then nd I: f(5:1:)dac. (f) Find f satisfying f'(a:) = cosa: +x2 + 1, f(0) = 0. [3) Compute the following limits. When using L'Hopitals Rule, please specify the type of indeterminate form. 1 b l' 3 ( ) $33}: COS(\\/a_:) , tans: a: (c) 1m , ln(1 3:) sina: (d) 3213(1) 1 0032 a: (4) Show, using implicit differentiation, that the derivative of arctan is 1 + 2. a: [5) A man walks along a straight path at a speed of 4 ft/s. A spotlight is located on the ground 20 ft from the path and is kept focused on the man. At what rate is the spotlight rotating when the man is 15 ft from the point on the path closest to the light? (6) Show with justication that the equation :54 + 4:1: 1 = 0 has exactly 2 solutions