Math3APracticeFinalWinter09

Math3APracticeFinalWinter09 - x 2 + xy + y 2 = 3 at the...

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Math 3A Winter 2009 Final Exam-Practice Name: Perm #: Lecture Time: TA’s Name: Discussion Time: DIRECTIONS: Please do not open your exam until you are instructed to do so. Write your name and fill in the blanks corresponding to your perm number, lecture time, TA’s name, and discussion time. Show all your work. Answers without explanation will not receive credit. Scratch paper has been provided for your convenience, however it will not be graded. Calculators, notes and formula sheets are not allowed. Clearly box your answers. There are nine problems on the exam and each is worth 5 points. Problem Score Problem Score Problem Score 1 /5 4 /5 7 /5 2 /5 5 /5 8 /5 3 /5 6 /5 9 /5 Total /45 1
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1. Find the limit. (a) lim x 3 x + 6 - x x 3 - 3 x 2 (b) lim θ 0 cos θ - 1 θ (c) lim x 0 + (cos x ) 1 /x 2 (d) lim x 0 ± 1 x - 1 | x | ² (e) lim x →∞ ( e - 2 x cos x ) 3
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2. Prove that the equation cos x = x 3 has at least one solution. 5
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3. Find the equation of the tangent line to the curve
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Unformatted text preview: x 2 + xy + y 2 = 3 at the point (1 , 1). 7 Scratch 8 4. Find d dx (sec-1 x ) Give your answer in terms of x , only. 9 Scratch 10 5. Let f ( x ) = 1 / (2-x ) . Find f (100) (1) . 11 Scratch 12 6. Find the absolute maximum and absolute minimum of f ( x ) = 2 cos x + sin 2 x on [0 ,/ 2] . 13 Scratch 14 7. Find the number c that satises the conclusion of the Mean Value Theorem for f ( x ) = e-2 x , [0 , 3] 15 Scratch 16 8. For what values of the numbers a and b does the function f ( x ) = axe bx 2 have the maximum value f (2) = 1? 17 Scratch 18 9. A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 30 ft, nd the dimensions of the window so that the greatest possible amount of light is admitted. 19...
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This note was uploaded on 04/09/2011 for the course MATH 3a taught by Professor Shu during the Winter '08 term at UCSB.

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Math3APracticeFinalWinter09 - x 2 + xy + y 2 = 3 at the...

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