This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Exam I Sept 13, 2007 MAC 2312 S Hudson Problems 48 are worth 10 points each. 1) [20 points; 4 each] Short calculations. Notice that the second sum starts at 11. 20 k =1 k 2 = 30 k =11 k = 2007 k =1 ( 1 k 1 k +1 ) = d dx [ R x 3 ln( t ) dt ] d dx [ R x 2 1 ln( t ) dt ] 2) [15pts] Compute these integrals: R / 4 sec 2 ( ) d . R 3  ( x 2)( x + 1)  dx R sin 2 3 x dx 3) [15pts] Answer True or False: In uniformly accelerated motion, velocity is constant. For continuous functions, R b a f ( x ) g ( x ) dx = ( R b a f ( x ) dx ) ( R b a g ( x ) dx ). If we used only regular partitions of [a,b], then the phrase max 4 x k 0 would be equivalent to n + . If f is bounded on [a,b] it is integrable there. If we use the Right Endpoint Rule to approximate R 2 1 1 t dt , with n = 100, our estimate will be too small. 4) Find all values of x * that satisfy the MeanValue Theorem for Integrals, for f ( x ) =  2 x  on the interval [1,3]. 5) Use lefthand endpoints in a regular partition, with n=3, to approximate the area under f ( x ) = x 2 + 1 on [1 , 4]....
View Full
Document
 Summer '08
 Storfer
 Calculus

Click to edit the document details