Math 131 Exam 1 Review for Week in Review 1 Find the domain of each function a f x ln x 2 d f x f x 2 ln x b x2 5x 6 e f x f x c 1 ln x 3 1 x2 5x 6 2 Find the range of each function a f x 5e x 6 c f x x 2 9 f x 3 ln x 4 b f x d 1 x 1 2 3 Write the basic function and the transformations which result in the given function a f x 3e x 2 c f x 4 x 5 3 8 b f x 5 e x 1 7 d f x ln 2 x 4 Find the inverse function to the given function Give the domain and range of the function and its inverse a f x 3e 4 x 2 c f x 2 x 2 8 restricted to 0 b f x 2 x 2 8 restricted to 0 d f x ln x 5 Find f g x and g f x a f x 3 2 x g x ln x b f x x 2 1 g x x 6 A culture grew exponentially so that at t 0 hours there were 15 g and at t 5 hours there were 20 g a Write the formula for the weight at t hours b Find the weights at t 0 at t 15 and at t 17 c Write the formula in base e and find the continuous growth rate 7 Solve each equation for x a 9 x 3 x 2 28 0 b e 2 x 5e x 150 8 A principle of 20 000 was invested at the annual interest rate of 3 compounded continuously Find the amount in the account after 20 years 9 The half life of a certain drug in the body is two days If 16 mg are taken on day 0 in how many days will the amount remaining be 1 mg 10 Evaluate lim f x x a a c f x f x x2 x 6 2x2 4x x2 2x 3 x 1 3 lim f x Does lim f x exist x a a 2 x a b f x a 1 d f x x2 x 6 2x2 4x sin 3 x x a 0 a 0 11 Find all discontinuities of f x if any f x a x 1 x2 1 2 x 2x 3 f x 0 2 b x2 2x 3 x 1 and x 3 1 x or x 3 12 Find the value of A which makes f x continuous for all x Ax 7 f x 2 x A 13 a d lim x lim x 2 x 3e x 5 4 ex x 5 x3 x f lim x 2 x 4 10 x2 2x b e lim e x lim x x2 4x 1 sin x c 4 x 3 12 x 2 1 25 3 x 3 lim x 8 x 5 4 x 4 27 3x2 2 x
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