1. What is the visual meaning of a determinant ?

  2. What is larger ep or pe?

  3. òudv = uv - òvdu

  4. (b-a)/b < aòb 1/x dx < (b-a)/a

  5. Show that oòx/2 sinx dx + oò1 arcsinx dx = p/2
  1. Show that 1 + 2 + 3 + . . . + n = n(n + 1)/2

  2. Show that 1 + 2 + 3 + . . . + n + . . . + 3 + 2 + 1 = n2

  3. Show that 1 + 3 + 5 + . . . + (2n - 1) = n2

  4. Show that 1/2 + 1/4 + 1/8 + . . . + 1/2n = 1

  5. You have a 3-gal and a 5-gal jugs. How can you measure off 4 gal of water?


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