1. Explain two of the benefits of rationalizing denominators. 2. What does the rate of change of the position function represent? 3. Determine lim +3 3x-8 4x-12' if it exists. 10 4. Determine f'(x) if f(x) = 3-x* 1 5. Determine the coordinates of the point(s) on the graph of y = 3x-- at which the slope of the tangent is 7. x 6. Determine the slope of the tangent line to y= 3-x 2x-3 at (0, -1). 7. The function E(x) = 50x2+40x+33 x-1 models a company's expenses in thousands of dollars per 1000 units to produce touch sensitive screens for small electronics. x represents thousands of screens. At what rate is the expense per screen changing when the company produces 3000 screens? Problem x-9 8. Make a conjecture about the value of lim Describe a reason why the limit may in fact exist. 9. Determine lim 125-x x-125 T Explain each step. x-5 10. a. Use the limit definition to determine the derivative of f(x) = x-1. 11. b. Determine the slope of the tangent to f(x) at (10, 3). a. Determine the derivative of f(x) = (x + 1) (3x-5)*. Write your answer in simplified factored form. b. Determine the value(s) of x for which the graph of f(x) has a horizontal tangent. 12. a. Determine f'(x) if f(x) = (8r2 +x). Write your answer in simplified form. b. Determine f ^{ } }).