Past Exam for MATH 11 - Calculus with Applications at UC Santa Cruz (UCSC)

Exam Information

Material Type:Final
Class:MATH 11 - Calculus with Applications
University:University of California-Santa Cruz
  • Autonomous Differential Equation
  • Either...or
  • Temperature
  • Approximation
  • Proportionality
  • Trigonometric
  • Smallest Value
  • Following Functions
  • Eigenvalues
  • Initial Value
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Sample Document Text

Math 11B Final Review Problems Note: these problems represent some of the topics that were covered since Midterm 2. Bear in mind that the final will be comprehensive, with a slight emphasis on the most recent topics. See earlier review problems and solutions to Midterms 1 and 2 for review of earlier topics. 1. Use Integration by parts to prove the following formula: ∫∫ −−= dxexanexadxex axnaxnaxn 11 . 2. Find the linear approximation to xexf =)( for x near 2. 3. Find the thn degree Taylor polynomial of the following functions )(xf for x near a. a. xexf =)( , 5=n , 0=a b. xexf =)( , 5=n , 1=a c. 2)( xexf −= , 10=n , 0=a (Hint: substitute into your answer to part a) Note: in an earlier version of this document, the hint said part b, which was an error. Let me expand on the hint a little. Take your answer for part a (not b), and replace x everywhere you see it by 2x− . This is much easier than taking 10 derivatives of 2xe− . d. xxf sin)( = , 7=n , 0=a e. xxf += 1)( ,...

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