166 Calculus,
Practice Exam 3.

(* The actual Exam 3 is Friday, April 4, 2003  7:30 to 9:00 AM *) 

Sections 8.8-8.9, 9.3-9.4, 11.1-11.4

Instructions:  You are welcome to check your answers with your calculators.  
But you will not be given full credit unless your work is clear, complete, 
and correct. 


1.  Write the equation of the circle given that the segment between

(2,4,8) and (1,2,3) is a diameter.

2.  Write the equation of the plane containing (2,3,4), (1,1,1) and (5,0,5).


3.  Write the equation of the line containing (1,2,3) and (5,6,3).

4.  The points A = (1,3,9), B = (2,1,3), C = (0,9,9) are a triangle.

Find the angle at A. 

5.  P is the point (2,3,4).  W is the plane 2x + 3y + z = 7. 

(a)  Find the distance from P to the plane W. 

(b)  Find the point on the plane W closest to P.


6.  P is the point (3,1,1). L is the line  x  = 1 +   t
                                           y =  5 + 3 t
                                           z =  7 - 4 t 

(a) Find the distance from P to L.

(b) Find the point on L closest to P.

7.  L1 is the line  x = 1 +   t          L2 is the line  x = 5 +   t
                    y = 2 -   t                          y = 6 - 3 t
                    z = 3 + 2 t                          z = 4 + 2 t

(a) Find the distance between L1 and L2.

(b) Find the point on L1 and the point on L2 which are closest together.

8.  Find n so that the error from Simpson's rule for

x=10
 INT   Sin[x^2]  dx   is less than or equal to 0.0001 .
 x=0
                  5
            K(b-a)              (4)
| Es | <=  -----------       | f     |  <= K
                  4
             180 n


                  3
            K(b-a)              (2)
| Et | <=  -----------       | f     |  <= K
                 2
             12 n


9.  Use the Trapezoid rule and Simpson's Rule to

compute the area of this lake.


                                      .
                                 .  ' | ' . .
                             . |      |      |'.
                         . '   |      |      |   ' .
                   .  ' |      |      |      |      |'.
              . ' |     |      |      |      |      |   ' .
            .'    |     |      |      |      |      |      |'.
          .'     30    35     45     50     45     35     10  '.
          :.......|.....|......|......|......|......|......|.....:|
          |<-10->|<-10->|<-10->|<-10->|<-10->|<-10->|<-10->|<-10->|


10.  Find the area of the surface obtained by rotating the

          3    2
curve   (t  , t  )    0 <= t <= 1  about the x axis.