advertisement

Math 142 In Class Exam 3 Review 1. Find each indefinite integral. a) c) e) x 2 3 4 ( x 5 ) dx 12 x 2 8x x 3 x 2 20 ( x 5) 2 b) dx (x d) 3 3 x 20 9x x 2 dx 3 2 x )( x 7 ) dx f ) (x 2 4 dx 2 x )e 5 2 x 5 x 12 2. a) A marginal average profit function is dx MAP 0 . 15 3000 x The average profit per unit if 100 units are produced is $55. Find the profit function. b) Find dy y ( t ) if dt dy c) Find y(t) if t t 2 4 te t 1 2 and y ( 0 ) 6 . and y ( 0 ) 3 dt 3. Find the left and right hand Riemann sums using 5 equal subintervals of [ 1, 3] for f (x) 1 . x b 4. Show that xe x e x is an antiderivative for xe x and evaluate xe x dx . a 5. Evaluate each. 4 a) f ( x ) dx 1 2 1 x f (x) x 1 1 x 1 1 x 4 b) t t 2 1 dt 4 c) x 2 e t dt dx 0 d x d) d t2 dt dt e 0 6. a) Find the area between the graphs of f ( x ) 2 x 2 7 x 12 and g ( x ) x 2 6 x for x between -5 and 5. b) Find the area between the graphs of f ( x ) 2 x 2 7 x 12 and g ( x ) x 2 6 x . 7. Find the consumer surplus and producer surplus at equilibrium for demand and supply prices a) D ( x ) 46 0 . 02 x 2 S ( x ) 10 0 . 02 x 2 b) D ( x ) 46 0 . 01 x 2 S ( x ) 10 0 . 03 x 2