Practice TEST 2   

The actual midterm is Friday, October  9, 2009

During Class 7:30 to 9:00 AM


Practice Test

1.  Find the Oblique asymptote to

             3      2
            x   + 4x   + 17 x + 5
     f(x) = -------------------
                2
               x  + 3 x + 2













                                2
2.  Find     Limit       Sqrt[ x  + 2 x + 1 ] - x
          x->Infinity


















3.  Find the equation of the tangent line to

      3  2     2  2
     y  x   + y  x   + 4 x y = 6   

    
    at the point (1,1). 

















4.   A 26 foot ladder is leaning against a wall. 

     The bottom is 10 feet from the wall and moving

     towards the wall at 1 ft/sec.  How fast is the

     top of the ladder moving up the wall.



















                                               2
                                          2 m s
5. The equation for horsepower is   hp = -----------------
                                                3
                                           550 t

Where m = weight/32;  s = distance in feet, and t = time in

seconds.  If  weight = 1600 +/- 8  lbs.   s = 990 ft +/- 5 ft.

t = 5 +/- 0.01 sec.

(a)  Find the horsepower.

(b) how does the horsepower change due to the error in weight?

(c) how does the horsepower change due to the error in distance?

(d) How does the horsepower change due to the error in time?













                       /
6.   If f(5) = 14 and f (5) = 32.  Use differentials to approximate

f(14.5).















7.    Your balloon is falling at a constant rate of 30 ft/sec.

When the balloon is at 500 feet, you untie 100 lbs of sand.

(a)  How long till the sand hits the ground.

(b)  What is the velocity of the sand when it hits the ground.













8. Gravel is being dumped from a conveyor belt at the rate of

30 ft^3/min and its coarseness is such that it forms a pile

in the shape of a cone whose base diameter and height are always

equal.  How fast is the height of the pile increasing when

the pile is 10 feet high.




















In problems 9 through 17, Find the following derivatives.

              x Sin[x]
9.    f[x] = ----------- 
                Cos[x]







               
10.    f[x] =  Sec[x] + Tan[x]












                 2  4
11.   f[x] = (3+x  )  







                 Pi     2
12.    f[x] =   2    + x  








                   2
13.   f[x] =  Sin[x   + 2x]








              2
14.   f[x] = x  Sin[x] + x Cos[x]









15.   f[x] = Sqrt[1+Sqrt[x]]








                   8
16.   f[x] =   ------------
               Sqrt[4+3x]








17.   f[x] = Sqrt[1+2 Tan[x]]