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1. Let f be defined by

   f(x) = ì í î 5-x2, if   -1 < x < 1 2(2-x), if   x ³ 1.

   1. Sketch the graph of f.
   2. Determine the domain and range of f.
   3. Is f continuous at the points x = -1,0,1? Verify your answer.

2. Using the properties of limits, find the the following limits putting in each step:
   1. lim_{x® 3} [(x²-4x+3)/(x²-9)]
   2. lim_{x® 2} [(x²-4x+3)/(x²-9)]
   3. lim_{x® 0} [tan(x)/x cos(x)]

3. Using the definition of derivative and the properties of limits, compute the derivative of f at x = 2 where f is given by

   f(x) = x2+x-3.

4. Let

   f(x) = 2x3-6x-2.

   1. Compute the slope of the tangent line to the graph of f when x = 1.
   2. Give the equation of the tangent line to the graph of f at the same point.
   3. For which values of x is the tangent line horizontal?

5. Using the properties of derivatives, determine the derivatives of each of the following functions:
   1. g(x) = (2x²-3)(1-2x+x²)
   2. f(x) = x² e^x -2x³        (Hint: You can use D_x(e^x) = e^x)
6. [EXTRA CREDIT]
   Using the definition of `limit', prove that

   lim x® 0  x2 = 0.