Show all work for credit. Do all your work neatly on the paper provided. Write your name on each sheet you turn in. I will not grade any work done on the test sheet. When you are finished turn in all sheets including the test. Good Luck.

1. Given that

                2x+3    x £ -1

   h(x) =

                 3-x     x > -1

   find lim_{x ® -1⁺}h(x) and lim_{x ® -1^-}h(x).

2. Find the piecewise definition of |2x²-5x-3|.

3. Find the following limits:

   1. lim_{x ® -3}[(x²-9)/( x+3)].

   2. lim_{x ® 3}[1/( x³-8)].

   3. lim_{x ® 2}(x³-7)(x²-x+1).

   4. lim_{x ® ¥} [(5x-x²)/( x²+3x)].

   5. lim_{x ® 7^-} [(x²+4)/( x-7)].

   6. lim_{x ® 2} (2x-3)¹¹.

4. Calculate lim_{x ® -¥}(x-[Ö(x²-3x)]).
5. Given f(x) = ax³ find f¢(x).
6. Find the equation of the tangent line to the graph of f(x) = x³ at x = 2.
7. Given the position function s(t) = 2t²-t+1 find the instantaneous velocity at t = 2.
8. Find the collection of open intervals on which the function f(x) = [(2x-1)/( x²+x-2)] is continuous.
9. In each case find a function which has the desired property:

   1. The limit as x approaches 2 does not exist.
   2. The derivative does not exist at x = 2.
   3. The limit as x approaches 2 exists but f is not continuous at x = 2.

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