Exam 1 Review Problems 1. Find the derivative of the following functions: f ( x) sin x f ( x) cos x f ( x) tan x f ( x) sec x 1 e) f ( x) x f) f ( x) ln x g) f ( x) arcsin x h) f ( x) arctan x a) b) c) d) 2. Find the antiderivative of the following functions: a) b) c) d) e) f) g) h) i) j) k) l) m) f ( x) sin x f ( x) cos x f ( x) tan x f ( x) sec x f ( x) sec 2 x f ( x) sec x tan x 1 f ( x) x f ( x) ln x f ( x) arcsin x f ( x) arctan x 1 f ( x) 1 x2 1 f ( x) 1 x2 1 f ( x) 16 x 2 3. If F (x) is an antiderivative of f (x) , evaluate f (ax b)dx , where a and b are constants. Now, evaluate the following: 1 a) b) ax b dx sin(ax b)dx Page 1 of 3 c) tan(ax b)dx sec (ax b)dx e dx 2 d) e) axb 4. Complete the following trigonometric identities. a) Power Reduction Formulas: sin 2 x ________________ cos 2 x ________________ b) Double Angle Formulas: sin(2 x) _______________ cos(2 x) _______________ 5. Answer \"True\" or \"False\" for the following problems: a) b) c) x dx x xdx xdx ( x x )dx xdx x xdx xdx xdx xdx sin 3 x C 3 2 2 e) sec x 1 tan x d) f) g) h) i) j) 2 sin xdx x2 4 x 2 9 3 x 22 x 2 4 3 0 0 0 0 3 Page 2 of 3 1 x 2 2 x 1 1 2 x l) x2 x2 1 x2 1 1 1 2 m) x x x x x x x x x 1 2 x n) 2 x 1 x 1 x k) Review section at the end of Stewart, 8th edition, Chapter 7, p.537 Exercises: 6,7,9,10,11,12,13,14,15,16,18,19,21,23,25,26,27,33,37,41,43,45,47,71 Review section at the end of Stewart, 8th edition, Chapter 8, p.581 Exercises: 1, 2, 4, 9 Also, see the handout \"Integrals, Derivatives, Identities You Should Know\" - also posted on the eLearning course homepage. Page 3 of 3