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Unformatted text preview: | x-1 | x-1 , if x 6 = 1 , 2 , if x = 1 . 9. (3 Marks) Find the critical values of f ( x ) = x 4 / 3-x 1 / 3 . (a) Identify the intervals on which f is increasing. (b) Identify the intervals on which f is decreasing. (c) Are there any extrema? 10. (4 Marks) Using L’Hopital’s rule, ﬁnd the following limits, if they exist. (a) lim x → e x-(1 + x ) x 3 = (b) lim x →∞ x-4 / 3 sin(1 /x ) = (c) lim x → + 1-ln x e 1 /x = (d) lim x →∞ x + sin2 x x = 11. (2 Marks) A crystal has the shape of a perfect circular cone. Its height is 250 mm and is increasing at a rate of 4 mm per century. Its radius is 45 mm and is decreasing at a rate of 0.4 mm per century. (a) Is its volume increasing or decreasing? (b) At what rate? [Hint: You may use the fact that the volume of a circular cone is V = 1 3 πr 2 h , where h = height, r = radius.]...
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- Spring '07
- lim, Continuous function