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Unformatted text preview: Final Review Answers p. 1 Disclaimer: This answer sheet may contain errors, hopefully there are not many. 1. a. 1 x +2 = pos # which means that ) 2 ( 2 + = + ξ ξ and you cancel b.-1 x +2 = neg # which means that ) 2 ( 2 +- = + ξ ξ and you cancel c. 1 divide each term by the highest power in the denominator which is x (Note: 2 x x = ) d. divide each term by the highest power in the denominator which is x 2 e. 6 1- you get , so use L’Hopital’s Rule repeated until you no longer get f. DNE x y sin = does not “settle down” to a single value and continually oscillates 2. a. 3 1 see problem 1c b. DNE Compute 4 5 lim 4- + → ξ ξ and 4 5 lim 4-- → ξ ξ and see that they are not the same value c. DNE ( 1 3 lim ) ( lim 2 2 2 =- = + + → → η η θ η η 3 1 lim ) ( lim 2 2 = + = + + → → η η θ η η ) d. 5 Compute the left- and right-hand limits e. 4 1- Simplify by first using a common denominator 3. a. b. 4. Write the equation as cos =- ξ ξ , then show that for some value of x x x- χοσ = neg # and for a different value of x x x- χοσ = pos #. (Hint: find an x-value that gives these two results). Then explain how you know that x x- χοσ is continuous and use the Intermediate Value Theorem to claim that for some of x , cos =- ξ ξ . (Or in terms of the original problem there is some x-value where x x = χοσ .) 5. a. 2 2 ) (- = ′ ξ ξ φ b. 2 1 ) ( x x f- = ′ 6. 2 ) 2 sin ( cos ×- + = ′ ξ ξ ψ and 2- = ÷ ′ π ψ . Final Review Answers p. 2 Disclaimer: This answer sheet may contain errors, hopefully there are not many....
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This note was uploaded on 10/17/2011 for the course MTH 133 taught by Professor Staff during the Fall '08 term at Michigan State University.
- Fall '08