Exam 1 Sp22-122(Review)

Math 1331 Exam 1 Name: _______________________ Turn in Scantron and exam. Make sure to put name and R number on scantron. 1. What is the relationship between cost, fixed cost, and variable cost? 2. What is the relationship between price( p ) and revenue( R )? Here x represents the number of units. 3. What is the relationship between cost, revenue, and profit? 4. What does the derivative of a function represent graphically? 5. Choose the statement of definition of derivative. 6. Choose the correct interval notation for the inequality expression or . 7. Choose the correct interval notation for the inequality expression , {All real number greater than or equal to -2.} a. Cost = fixed cost * variable cost c. Cost = fixed cost + variable cost * number of units d. Cost = a x 2 + bx + c b. Cost = m x + b c. R = p − x d. R = px b. R = p x a. R = px + b d. R = PC b. P = R − C c. P = RC a. P = C − R a. Slope b. Area c. Perimeter d. Area under the graph c. f ′ ( x ) = lim h → 0 f ( x + h ) − f ( x ) h d. y = a x 2 + bx + c b. x =   − b ± b 2 − 4 ac 2 a a. y = m x + b x <   − 4 x > 9 d. None of the above a. ( −∞ , − 4) ∩ (9, ∞ ) b. ( −∞ , − 4) ∪ (9, ∞ ) c. [ −∞ , − 4 ] ∪ [ 9, ∞ ] a. ( − 2,  ∞ ) b. ( −∞ ,   − 2) d. [ − 2 , ∞ ) d. [ −∞ , − 2 ] pg. TTU 1 Math and Statistics Dept Spring 2022

8. Choose the correct interval notation for the inequality expression , or or . a. b. c. d. 9. Solve the rational equation: a. b. c. d. e. None of the above Directions : For questions 10 through 12, Suppose a company has fixed costs of $65 and variable cost per unit of where x is the total number of units produced. Suppose further that the selling price of its product is x dollars per unit. 10. Write an equation representing the total cost function. a. b. c. d. e. None of the above x <   − 7 2 < x < 6 x > 10 ( −∞ , − 7) ( 2,6 ) (10, ∞ ) ( −∞ , − 7) ∪ ( 2,6 ) ∪ (10, ∞ ) 3 x x − 2 = 1 2 + 8 4 x − 8 x = − 3 20 x = 1 x = 2 5 x = 2 (1/4) x 2 + 50 x 75 − 3 4 x C ( x ) = 1 4 x 2 + 50 x + 65 C ( x ) = 1 4 x + 50   C ( x ) = 75 − 3 4 x C ( x ) = 75 x − 3 4 x 2 pg. TTU 2 Math and Statistics Dept Spring 2022

15. What is the marginal profit ? a. b. c. d. e. None of the above ___________________________________________________________________________________ Directions : For questions 16 and 17, The profit function for a certain commodity is, 16. Factor the profit function. a. b. c. d. e. None of the above 17. Find the level of production that yields the break-even points. a. units b. units c. units d. units e. None of the above __________________________________________________________________________________ Directions: For questions 18 through 22, use the graph to find the limits at the given points from the given directions. ¯ MP ¯ MP = 1 4 ¯ MP = − 4 ¯ MP = − 1 4 ¯ MP = 4 P ( x ) = x 2 − 15 x + 56. P ( x ) = ( x − 7)( x − 8) P ( x ) = ( x + 7)( x + 8) P ( x ) = ( x − 7)( x + 8) P ( x ) = ( x + 7)( x − 8) x =   − 7,   − 8 x = 7,   8 x = 7,   − 8 x = − 7,8 pg. TTU 4 Math and Statistics Dept Spring 2022

18. Find the limit: 19. Find the limit: 20. Find the limit: 21. Find 22. Is continuous at ? a. Yes, because both the limit exists, and function exist, and they are equal. b. No, because the function value does not exist. c. No, because the limit does not exist. d. No, because the limit value of the function. e. None of the above _____________________________________________________________________________________ 23. Estimate the limit. 24. Estimate the limit. lim x → 0 − f ( x ) a. 3 b. 0 c. 1.5 d. DNE e. None of the above lim x → 0 + f ( x ) a. 3 b. 0 c. 1.5 d. DNE e. None of the above lim x → 0 f ( x ) a. 3 b. 0 c. 1.5 d. DNE e. None of the above f (0) a. 3 b. 0 c. 1.5 d. DNE e. None of the above f x =   0 ≠ lim x → 3      x − 3 x 2 − 2 x − 3 a. 1/4 b. 0 c. 1 d. DNE e. None of above lim x → 3     x + 3 x 2 − 9 a. -1/3 b. 1/6 c. 0 d. DNE e. None of above pg. TTU 5 Math and Statistics Dept Spring 2022

Directions: For questions 29 and 30, The average monthly sales volume (in thousands of dollars) for a firm depends on the number of hours x of training of its sales staff, according to the following. 29. Find . a. None of the above 30. Find to the nearest integer. a. None of the above ___________________________________________________________________________________ Directions: For questions 31through 35 , Use 31. Evaluate . 32. Expand S = S ( x ) = 15 x + 50 + x 15 ,           15 ≤   x ≤ 100 lim x → 15 + S ( x ) a. 52 thousand dollars b. 80 thousand dollars c. 57 thousand dollars d. 50 thousand dollars lim x → 100 − S ( x ) a. 52 thousand dollars b. 57 thousand dollars c. 80 thousand dollars d. 50 thousand dollars f ( x ) = x 2 − 5 x f ( x + h ) b. x 2 − 5( x + h ) c. x 2 − 5 x + h a. ( x + h ) 2 − 5( x + h ) d. ( x + h ) 2 − 5 x f ( x + h ) − f ( x ) h a. x 2 − 5 x − 5 h − x 2 + 5 x h c. x 2 + 2 x + h − x 2 + 5 x h b. x 2 + h 2 − 5 x − 5 h − x 2 + 5 x h d. x 2 + 2 xh + h 2 − 5 x − 5 h − x 2 + 5 x h pg. TTU 7 Math and Statistics Dept Spring 2022

33. Cancel alike terms in . 34. Give the final answer for 35. Take the limit f ( x + h ) − f ( x ) h b. 5 h h c. 2 xh + h 2 − 5 h h a. h h d. h 2 − 5 h h f ( x + h ) − f ( x ) h . d. h a. 2 x + h 2 − 5 c. 2 x + h − 5 b. 5 lim h → 0 f ( x + h ) − f ( x ) h . b. 1 c. 0 d. 5 e. None of the above a. 2 x − 5 pg. TTU 8 Math and Statistics Dept Spring 2022