Mathematics 210 - Spring term 2003 - Mid-term examination

You may use only pen and paper and a calculator for this exam.

• Question 1.

  Load the spreadheet answer.m210.mt.1.ms. Use linear interpolation to estimate f(1.67), and place the answer, with some indication of work, clearly on the spreadsheet. Estimate that value of x such that f(x) = 2.367.

  Save this as m210.mt.1.ms. Then clear the spreadsheet.
  
  

• Question 2.

  Calculate the integral of sin(x)/x from 0 to 1 correctly to 4 decimals, using the trapezoid rule. Explain how you know the accuracy.

  Warning! Be careful about sin(x)/x when x=0! You will have to handle this as a special case.

  Save this as m210.mt.2.ms. Then clear the spreadsheet.
  
  

• Question 3.

  Use the spreadsheet to help you find the base 2 expression for 1/13 far enough until you can guess the repeating pattern. Indicate what the repeating pattern is in your own words. Label your answers and work carefully.

  Save this as m210.mt.3.ms. Then clear the spreadsheet.
  
  

• Question 4.

  Use the spreadsheet to calculate and graph the probabilities of getting a score of 3 ... 18 when you throw three dice.

  Save this as m210.mt.4.ms. Then clear the spreadsheet.
  
  

• Question 5.

  Use the asymptotic formula to give a quick estimate of the area under the curve
  y = e^-x2/4/ between x=0 and x = 6. (Note: you will have to relate this curve to the standard bell curve by scaling.)

  Save this as m210.mt.5.ms.