MATH 1171: Calculus for Business and Management Sciences A1-1 Assignment 1: Limits and Differentiation (80 marks total) Your mark will be given as a percentage. [10 marks] 1. (4 marks) a. Make an inputoutput table in order to investigate the behaviour of as approaches 9 from the left and right. . (1 mark) b. Use the table to estimate lim (5 marks) c. Using an appropriate factorization, find an exact value for . lim [10 marks] 2. 5. Find lim Sketch the graph of , if it exists. If the limit does not exist, explain why, using onesided limits. [10 marks] 3. 2 Consider the function, 4 0 0 (4 marks) a. Sketch the function. (3 marks) b. Find lim (3 marks) c. Is continuous at 0? Explain, using the definition of continuity. , lim TRU Open Learning , and lim . A1-2 [10 marks] Assignment 1: Limits and Differentiation 4. Consider the function , graphed below. Find the following limits. If the limit does not exist, explain why. i.lim iii.lim v. lim vii. lim ix. lim ii.lim iv.lim vi. lim viii. lim x. lim [8 marks] 5. Let (4 marks) a. Sketch the graph of F. 5 2 2 (4 marks) b. Is F continuous at 2? Explain why or why, not using the definition of continuity. [7 marks] 6. Suppose that the cost of production of items is given by 40 100, where is in hundreds of dollars. 0.1 (2 marks) a. What is the overhead cost in dollars? (3 marks) b. Find the average rate of change of as changes from 200 to 300. (2 marks) c. Explain what the number in b. represents. TRU Open Learning MATH 1171: Calculus for Business and Management Sciences [10 marks] 7. For 2 3, (6 marks) a. Find the simplified form of the difference quotient. (2 marks) b. Find 2 . (2 marks) c. Find an equation of the tangent line at x = 2. [10 marks] 8. For (6 marks) a. Find the simplified form of the difference quotient. (2 marks) b. Find 1 . (2 marks) c. Find an equation of the tangent line at x = 1. [5 marks] 9. For the graph in question 4, above, (2 marks) a. Give the xvalues at which h is not continuous. Explain briefly. (3 marks) b. Give the xvalues at which h is not differentiable. Explain briefly. TRU Open Learning A1-3 MATH 1171: Calculus for Business and Management Sciences A2-1 Assignment 2: Differentiation Techniques (80 marks total) Your mark will be given as a percentage. [10 marks] 1. Find the derivative in each case. You need not simplify your answer. (5 marks) a. (5 marks) b. [10 marks] 2. Find the derivative in each case. Simplify your answer. (5 marks) a. (5 marks) b. [10 marks] 3. Find an equation of the tangent line to the graph of: (5 marks) a. (5 marks) b. [10 marks] 4. For the function 3 . . 1 3 5 2 . . 7 at 2 1. 2 . at 7 24 11, (6 marks) a. Give all the points where the tangent line is horizontal. Note a point is given by two coordinates (_ , _). Give exact values. (4 marks) b. Give an equation of the tangent line at each of these points. Give exact values. [10 marks] 5. Find . for TRU Open Learning A2-2 [10 marks] Assignment 2: Differentiation Techniques 6. Suppose that the number of items sold after months is modelled by 500 25 2 (3 marks) a. Find ' 6 and ' 12 . (3 marks) b. Find " 6 , " 12 . (4 marks) c. What do the answers in a. and b. tell you about [10 marks] 7. Let and (6 marks) a. Find . (4 marks) b. Find 8 . [10 marks] 8. A company determines the cost, in thousands of dollars for 75. producing items is given by 500 ? 1. Let . If it plans to boost production in months from now according to the function 30 7, how fast the costs will be rising 6 months from now? TRU Open Learning