Name                                           :
Math 132 Quiz 1, January 23, 2002
  1. Values of the function f(x) are given in the table below.
    2. x 0 2 4 6 8 10 12
    f(x) 5 6 6.6 5.6 4 3 2
    1. Give a left hand sum that approximates  with 6 rectangles.

      2.  

       
       
       
       
       
       

    2. Plot the points (x, f(x)) in the table on the axes below and sketch in a nice function f(x) that goes through the points.
    3. Give a sum with 6 rectangles that is an over estimate of .

      4.  

       
       
       
       
       
       
       
       

    4. Draw in the rectangles you used in your over estimate sum (part c) on the plot of f(x) from part b.

      5.  

       

  2. Shown below is a plot of the function f(x) from x = 0 to 1.4. Use the graph to answer the following questions.
    1. Estimate f(0) and f(1.4).

      2.  

       
       
       

    2. Would a right hand sum with n rectangles over estimate or under estimate ? How do you know?

      3.  

       
       
       

    3. Give a decent estimate  of the average value of f(x) from x = 0 to 1.4.

      4.  

       
       
       
       
       
       

    4. If I wanted to know  accurate to three decimal places, how many rectangles would I use?

      5.  

       
       
       
       
       
       
       
       

  3. A warm beverge, whose temperature starts out at 72 degrees F, is put into a cold refrigerator at time t = 0 minutes. Suppose that the rate of change of the temperature of this beverage is approximated by the function r(t) = -3e -0.075t degees F per minute. Assume also that the variable t represents time, measured in minutes.
    1. What (use words to describe it) is represented by the quantity ?

      2.  

       
       
       
       
       
       
       
       
       
       
       

    2. Using your calculator (to evaluate some integral), what (approximately) is the temperature of this beverage after half an hour?