Work through the list without notes. Use a calculator only for the statement that says so. If you cannot do a statement, follow its link, then come back. Guide = study guide; Practice = practice questions. This topic is shared by Calculus AB and Calculus BC.
Understanding
- I can explain what a table of values tells me about a limit, and why the value at x = c does not matter. (Guide: “What a table can tell you”; Practice Q1)
- I can explain why a table suggests a limit but cannot prove it. (Guide: Worked example 3; Practice Q5(b), Q7(c))
- I can describe the three table patterns that suggest a limit does not exist. (Guide: “When a table suggests the limit does not exist”; Practice Q3, Q5)
Skills
- I can estimate a two-sided limit by reading a table from both sides towards c. (Guide: Figure 1 and Worked example 1; Practice Q1, Q4)
- I can estimate a left-hand or right-hand limit by choosing the correct rows of a table. (Guide: Worked example 2; Practice Q2)
- I can build my own table with a calculator, using x = c ± 0.1, c ± 0.01, c ± 0.001, in radian mode. (Guide: “Building your own table”; Practice Q7(a))
- I can state an estimate only to the decimal places on which the closest values from both sides agree. (Guide: Worked example 1, step 5; Practice Q7(b))
- I can write one-sided and two-sided limits in correct notation. (Guide: “A note on notation”)
Reasoning
- I can decide whether a two-sided limit exists by comparing my left-hand and right-hand estimates. (Guide: Worked example 2; Practice Q2, Q6(c))
- I can explain why averaging two different one-sided values does not give a limit. (Guide: “Common misconceptions”; Practice Q2)
- I can interpret a limit estimated from a table in a real context, with units. (Practice Q6(a), Q6(d))
All ticked? Move on to Topic 1.5, Determining Limits Using Algebraic Properties of Limits, or return to the Calculus AB roadmap or the Calculus BC roadmap.