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132_Final_Review_Solutions - Final Review Answers p 1...

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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. 0 divide each term by the highest power in the denominator which is x 2 e. 6 1 - you get 0 0 , so use L’Hopital’s Rule repeated until you no longer get 0 0 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 0 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 , 0 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. 0 2 ) 2 sin ( cos × - + = ξ ξ ψ and 0 0 2 - = ÷ π ψ .
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Final Review Answers p. 2 Disclaimer: This answer sheet may contain errors, hopefully there are not many. 7. π cm 2 /min ? = δτ δΑ when 50 = ρ 01 . 0 = δτ δρ Area of a circle: 2 r A π = Be sure to take the derivative of the Area equation BEFORE plugging in any numbers.
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