Homework for 9-19

  1. An 8 by 17 piece of cardboard is used to make an open topped box as in Example 1 of section 4.4. If squares of two units are cut out of each corner, the volume of the box is 104. Use Newton's method to find out the size of the squares that you'd have to cut out of the corners to get a box of volume 100. Make your answer accurate to within 3 decimal places.
  2. For each of the following functions, find a 4th degree polynomial P(x)=a_0+a_1x+a_2x2+a_3x3+a_4x4 such that P(0)=f(0), P'(0)=f'(0), P''(0)=f''(0), P'''(0)=f'''(0), and P''''(0)=f''''(0).
    1. sin(x)
    2. 1/(1+x2)
    3. arctan(x)