Work through the list without notes or a calculator. 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 why a filled point at x = c gives f(c) but does not decide the limit as x → c. (Guide: Worked example 1(b); Practice Q1)
- I can name three ways a limit can fail to exist and recognise each on a graph and in a table. (Guide: “One limit, four representations”; Practice Q4)
- I can explain why a table or a graph screen only suggests a limit, and give an example where it misleads. (Guide: “How a table can mislead”; Practice Q4, Q7(d))
Skills
- I can read left-hand, right-hand and two-sided limits from a graph with holes, jumps and isolated points. (Guide: Figure 1, Worked example 1; Practice Q1)
- I can estimate a limit from a table by following the trend from each side. (Guide: “Reading a table”; Practice Q2, Q6(a))
- I can find one-sided limits of a piecewise formula and choose a constant that makes the limit exist. (Guide: Worked example 3; Practice Q5, Q7)
- I can translate between a sentence and limit notation, in both directions. (Guide: “Reading a formula and reading words”; Practice Q7(c))
- I can find limits of sums, differences, products and quotients when one function is a graph and the other is a table or a formula, and I check that a bottom limit is not 0 before dividing. (Guide: Worked example 1(c), Worked example 2(c); Practice Q6(b), Q6(c))
Reasoning
- I can find a composite limit f(g(x)) by tracking the side from which g(x) approaches its limit. (Guide: Worked example 2(a); Practice Q3, Q6(d))
- I can split a limit into one-sided limits when a two-sided limit does not exist, and still reach a conclusion. (Guide: Worked example 1(d); Practice Q6(b))
- I can build a formula or describe a graph that matches a given list of limit statements. (Practice Q5)
All ticked? Move on to Topic 1.10, Exploring Types of Discontinuities, or return to the Calculus AB roadmap or the Calculus BC roadmap.