Unformatted text preview: on a straight shoreline, ﬂies to a point C on the shoreline, and then ﬂies along the shoreline to its nesting area D. Assume that the bird instinctively chooses a path that will minimize its energy expenditure. Points B and D are 13 km apart. If it takes 1.4 times as much energy to ﬂy over water as land, ﬁnd the distance between B and C. Ans. 5.1 km. 3. Use L’Hopital’s rule to ﬁnd the following limits. (a) lim x → π/ 2 1sin x 1 + cos2 x (b) lim x → ln(cos ax ) ln(cos bx ) , a, b > (c) lim x →∞ x tan 1 x (d) lim x → 0+ x a ln x , a > (e) lim x → 1 x 1 1x (f) lim x → + x sin x (g) lim x → ± sin x x ¶ 1 x 2 Ans. (a) 1 4 (b) a 2 b 2 (c) 1 (d) 0 (e) e1 (f) 1 (g) e1 / 6...
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 Spring '11
 phoon
 Energy, Order theory, Extreme value, Department of Mathematics

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