0000000000000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000000000000 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 000000000000000 TRU Open Learning 000000000000000 0000000 000000000000000 000000000000000 , and lim . 00000000000000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000 A1-2 Assignment 1: Limits and Differentiation [10 marks] 4. Consider the function , graphed below. Find the following limits. If the limit does not exist, explain why. ii.lim iv.lim vi. lim viii. lim x. lim i.lim iii.lim v. lim vii. lim ix. 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 00000000000000000 000000000000000000 00000000000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000000000000000000000000000 MATH 1171: Calculus for Business and Management Sciences A1-3 [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 0000000000000000 00000000000