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eq17.ms (706B)

      1 .TL
      2 Exam Questions 17
      3 .AU
      4 Lucas Standen
      5 .AI
      6 QMC
      7 
      8 .PP
      9 1)a)
     10 
     11 .EQ
     12 dx over dt = 2cos(t)
     13 .EN
     14 
     15 .EQ
     16 dy over dt = 2sin(2t)
     17 .EN
     18 
     19 .EQ
     20 dy over dx = 2cos(t) over 2sin(2t)
     21 .EN
     22 
     23 .EQ
     24 "when " t = pi over 6
     25 .EN
     26 
     27 .EQ
     28 dy over dx = {2cos({pi over 6})} over {2sin(2({pi over 6}))}
     29 .EN
     30 
     31 .EQ
     32 dy over dx = 1
     33 .EN
     34 
     35 .PP
     36 1)b)
     37 
     38 .EQ
     39 x = 2sin(t) 
     40 .EN
     41 
     42 .EQ
     43 x over 2 = sin(t)
     44 .EN
     45 
     46 .EQ
     47 1 = cos(2t)
     48 .EN
     49 
     50 .EQ 
     51 1 = 1 - cos sup 2 (t)
     52 .EN
     53 
     54 .EQ 
     55 y = cos sup 2 (t)
     56 .EN
     57 
     58 .EQ
     59 ({x over 2}) sup 2 + y sup 2 = 1
     60 .EN
     61 
     62 .EQ
     63 {x over 4} sup 2 + y sup 2 = 1
     64 .EN
     65 
     66 .EQ
     67 {x over 4} sup 2 - 1 = - y sup 2 
     68 .EN
     69 
     70 .EQ
     71 - {x over 4} sup 2 + 1 = y sup 2 
     72 .EN
     73 
     74 .EQ
     75 sqrt {- {x over 4} sup 2 + 1} = y sup 2 
     76 .EN
     77 
     78 .EQ
     79 -2 <= x <= 2 
     80 .EN
     81 
     82 .PP
     83 1)c)
     84 
     85 .EQ
     86 0 <= f(x) <= 1
     87 .EN
     88 
     89 
     90