Math 160

Exam 2

Fall 1999

 

  1. (48 pt) Find the derivatives of the following functions:

    2. a) b) c)

     

    d) e) is differentiable.

     

    f) g) h)

     

  2. (10 pt) Find the tangent line to the curve given by at the point (-2,-1).

    3.  

  3. (8 pt) Use linear approximations to estimate the value of .

    4.  

  4. (12 pt) Consider the function . Find all critical numbers and determine which (if any) are local extreme values.

    5.  

     

  5. (6 pt) Show that the radius of any circle is always perpendicular to its tangent line at that point.

    6.  

  6. (6 pt) Show that for any value of , the polynomial has one and only one root.

    7.  

     

  7. (15 pt) Two cars leave an intersection at the same time. The first car travels due north at 60 miles per hour and the second car travels at an angle 30° south of east at 45 miles per hour. How fast is the distance between the cars changing after 2 hours?

    8.  

  8. (5 pt) Show that any function of the form satisfies the equation