Directions: Show your work for full credit. Clearly indicate in your work the problem number and your answer.

1. Determine if the following limits exist and if so their value:
   1. lim_x®1 [(x²-3x+2)/(x²-1)]
   2. lim_x®¥ [(3x²+sin(x))/(1-x²)]
   3. lim_{x® 0} [(cos(x)-1)/x]
   4. lim_{x® 3^-} [1/(x²-9)]
2. Using the definition of derivative and properties of limits, compute f¢(1) where f(x): = 2+x-x².

3. Determine derivatives for each of the following functions:
   1. f(x) = (x²-1),
   2. [Ö(3x³-4x+1)]
   3. [Ö(sin(3x²))]

4. Using differentials, estimate cos(.05).

5. If the width of a rectangle is changing at a rate of twice its length and its length is changing at a rate of +5 cm/sec, then at what rate is the area of the rectangle changing?

6. Consider the function

   f(x) = x3-x2-x+2,        -2 £ x £ 4.

   1. Determine the intervals where f is increasing and where it decreases.
   2. Determine the critical points for the function.
   3. Determine the intervals where f is concave up and where it is concave down.
   4. Specify which points are local maxima, local minima, or inflection points.
   5. Sketch a graph of f using the information determined above.

7. Evaluate each of the antiderivatives:
   1. (2x²-3)(x²+2x)
   2. x[Ö(3-x²)]
   3. tan(x) sec(x)
8. Calculate the following definite integrals:
   1. ò₀² (x²-1)² dx
   2. ò₀¹ x[Ö(3-x²)] dx

9. Compute the area bounded by the curves y = x²-2 and 2x²+x-4.
10. Compute the volume of revolution about the axis of the curve

    y = x2-2x,     1 £ x £ 2.