Math 170 - fall 2015 - common final exam. E: none of a through d are correct. (b) with f and g functions of t, nd. A: f ef g + g ef g d dt(cid:16)ef g(cid:17). E: none of a through d are correct: (12 points) suppose the derivative of a function is df dt. 2 t3 cos(at + b) where a and b are constants. Write a possible function f : (12 points) consider the integral. Use the substitution u = x2 to transform this integral into a new integral using the variable u. 1: (12 points) a falling object"s velocity (in m/sec) at various times t (in seconds) is given in the table below. Use the tabulated data to address the questions that follow the table. dh dt dh dt (m/sec) t (seconds) 3 (a) estimate h on the time interval [1, 3].