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Math3APracticeFinalWinter09

Math3APracticeFinalWinter09 - x 2 xy y 2 = 3 at the point(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 ,π/ 2] . 13 Scratch 14 7. Find the number c that satisﬁes 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, ﬁnd the dimensions of the window so that the greatest possible amount of light is admitted. 19...
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Math3APracticeFinalWinter09 - x 2 xy y 2 = 3 at the point(1...

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