Fa08_Prelim2_sol - Math 1110 Prelim 2 Name Instructor...

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Math 1110 Prelim 2 October 30, 2008 Name: Instructor: Section: INSTRUCTIONS — READ THIS NOW This test has 6 problems on 12 pages worth a total of 100 points. Look over your test package right now . If you find any missing pages or problems please ask a proctor for another test booklet. Write your name, your instructor’s name, and your section number right now . SHOW YOUR WORK. To receive full credit, your an- swers must be neatly written and logically organized. If you need more space, write on the back side of the preced- ing sheet, but be sure to label your work clearly. YOU DO NOT NEED TO SIMPLIFY YOUR ANSWERS UNLESS EXPLICITLY INSTRUCTED TO DO SO. You have 1 1 2 hours to complete this exam. This is a closed book exam. You are NOT allowed to use a calculator. You may bring a single 3 × 5 inch index card of notes. All other aids are prohibited. Academic integrity is expected of all students of Cornell University at all times, whether in the presence or absence of members of the faculty. Understanding this, I declare I shall not give, use, or receive unauthorized aid in this examination. Signature of Student OFFICIAL USE ONLY 1. /16 2. /16 3. /18 4. /18 5. /18 6. /14 Total: /100
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Math 1110 (Fall 2008) Prelim 2 (10/30/2008) 2 Question 1. (16 points) Compute dy dx : (a) y = ln(cos( x )) y = 1 cos( x ) cos ( x ) = - sin( x ) cos( x ) = - tan( x ) (b) y = x sin( x ) for x > 0 ln( y ) = sin( x ) ln( x ), (ln( y )) = sin( x ) 1 x + cos( x ) ln( x ), y y = sin( x ) x + cos( x ) ln( x ), y = x sin( x ) sin( x ) x + cos( x ) ln( x ) .
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