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

## Exam Information

 Material Type: Final Professor: Staff Class: MATH 11 - Calculus with Applications Subject: Mathematics University: University of California-Santa Cruz Term: -- Keywords: Autonomous Differential EquationEither...orTemperatureApproximationProportionalityTrigonometricSmallest ValueFollowing FunctionsEigenvaluesInitial Value

## 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)( ,...

## Related Documents

Autonomous Differential Equation Exam
Autonomous Differential Equation Notes
Autonomous Differential Equation Exam
Approximation Notes
Approximation Notes
Autonomous Differential Equation Exam
Approximation Exam
Either...or Exam
Either...or Exam
Autonomous Differential Equation Exam
Provided That Notes
Either...or Notes
Unfortunately Exam
Temperature Quiz
Special Case Notes
Either...or Notes