This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Math 215 Fall 2011 Exam 1 Name: Lab section: Instructions: • The exam consist of 6 problems for a total of 68 points. Please look through the exam booklet and make sure it has eleven pages. The last page is blank and is to be used as scratch paper. • The exam duration is 90 minutes. • No calculators are allowed. • For multiple choice problems there is no partial credit. For all other problems, show all your work to receive full credit. • Make sure your answers are clearly marked (circled or boxed). Points Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Total You may find some of the following formulas useful (but probably not all of them) • sin 2 ( x ) + cos 2 ( x ) = 1 and cos(2 x ) = cos 2 ( x ) − sin 2 ( x ) • sin(2 x ) = 2 sin( x ) cos( x ) and sin 2 ( x ) = 1 − cos(2 x ) 2 • cos 2 ( x ) = 1 + cos(2 x ) 2 • cos( π/ 3) = 1 / 2 and sin( π/ 3) = √ 3 / 2. • cos( π/ 4) = √ 2 / 2 and sin( π/ 4) = √ 2 / 2. • cos( π/ 6) = √ 3 / 2 and sin( π/ 6) = 1 / 2. • cos(0) = 1 and sin(0) = 0. • d dx csc( x ) = − csc( x ) cot( x ) . • d dt sec( t ) = sec( t ) tan( t ) . • d dθ tan( θ ) = sec 2 ( θ ) . • d dr cot( r ) = − csc 2 ( r ) . • Arc length function: Length of curve from ( x ( α ) , y ( α ) , z ( α )) to ( x ( t ) , y ( t ) , z ( t )) is s ( t ) = integraltext t α  r ′ ( u )  du....
View
Full
Document
This note was uploaded on 01/28/2012 for the course MATH 215 taught by Professor Fish during the Fall '08 term at University of Michigan.
 Fall '08
 Fish
 Math, Calculus

Click to edit the document details