Review 1 - MAC2233 Chapter 2 Review 1 For the function f(x...

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MAC2233 Chapter 2 Review 1. For the function f ( x ) = x 2 - 3 x - 4 state the domain and evaluate the function at x = - 1 , 0 , a + h. 2. For the function y = 1 t 2 + t - 2 state its domain as well as the dependent and independent variables and evaluate the function at t = - 3 , 3 . 3. For the function g ( x ) = - 2 x + 5 , x ≤ - 3 0 , - 3 < x < 1 x 3 , 1 x evaluate the function at x = - 1 , 1 , 5 . 4. Given f ( x ) = x 2 + 1 and g ( x ) = x + 1 find f + g, f - g, fg, f/g, g f, f g and state the domain for each. 5. Find and simplify f ( a + h ) - f ( a ) h where f ( x ) = 2 x 2 - x + 1. 6. A manufacturing company has a monthly fixed cost of $100 , 000 and variable cost in dollars of V ( x ) = 0 . 000003 x 3 - 0 . 03 x 2 + 200 x where x denotes the number of units manufactured per month. The revenue for the company is given in dollars by R ( x ) = - 0 . 1 x 2 + 500 x. Find the profit function for the company and the profit when 1500 units are produced and sold each month. 7. A demand curve is given by p = d ( x ) = 60 - 2 x 2 and a supply curve is given by p = s ( x ) = x 2 + 9 x + 30 where x is the quantity demanded in thousands and p is the unit price in dollars. Find the equilibrium quantity and the equilibrium price. 8. Evaluate the following limits: f ( x ) = x + 1 x < 0 5 , x = 0 7 - x x > 0 1
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a. lim x →- 2 f ( x ) b. lim x 10 f ( x ) c. lim x 0 f ( x ) d. lim x 4 - f ( x ) e. lim x 0 + f ( x ) . 9. Evaluate the following limit: lim x 1 x +1 x 2 + x +1 . 10. Evaluate the following limit: lim t 3 t 3 - 9 t t 2 - 9 . 11. Evaluate the following limit: lim x →∞ - 2 x 4 +3 x 2 - 1 5 x 2 - 5 x +2 . 12. Determine the values of x at which the following function is continu- ous: f ( x ) = x 2 + 2 x - 4 x 0 ( x + 5) / ( x - 3) , 0 < x 4 9 x > 4 . 13. Consider the function
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Review 1 - MAC2233 Chapter 2 Review 1 For the function f(x...

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