Work through the list without notes. 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 state in my own words what lim (x → c) f(x) = R means, including “x close to c but not equal to c”. (Guide: “What a limit describes”)
- I can explain why a limit must be a single real number, and when to say a limit does not exist. (Guide: “What a limit describes”; Practice Q6(c))
- I can explain why the value f(c) does not decide the limit at c, and give an example where they differ. (Guide: “The limit ignores f(c)”, Figure 1; Practice Q2, Q6(d))
- I can explain why a missing value at c does not stop a limit existing. (Guide: three-cases table; Practice Q3)
Skills
- I can write a limit statement from words, with lim, x → c, the function and the value all in place. (Guide: “Reading and writing limit notation”; Practice Q1, Q5(a))
- I can read a limit statement aloud and in the arrow form f(x) → R as x → c. (Guide: notation table; Revision notes)
- I can interpret a limit statement in context, naming the input and output with units. (Guide: Worked example 1; Practice Q4, Q5(b))
- I can find a limit and a function value at the same point from a graph, and keep them separate. (Guide: Worked example 2; Practice Q6(a), Q6(b))
- I can say what limit a table of values suggests, and why it is only a suggestion. (Guide: “One limit, three representations”; Practice Q3)
Reasoning
- I can spot and fix notation errors: a missing x → c, a dropped lim, or swapped c and R. (Guide: “Common misconceptions”; Practice Q1, Q5(c))
- I can judge whether a written limit statement about a function is true or false, with a reason. (Guide: Worked example 2; Practice Q5(d))
- I can use the meaning of “as close as you like” to explain why a value close to R is not the limit. (Guide: background section, Figure 2; Practice Q7)
All ticked? Move on to Topic 1.3, Estimating Limit Values from Graphs, or return to the Calculus AB roadmap or the Calculus BC roadmap.