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 what x → a⁻ and x → a⁺ mean, and why the sign shows direction, not whether x is negative. (Guide: “A note on notation”)
- I can state the rule linking the two one-sided limits to the two-sided limit. (Guide: “One-sided and two-sided limits”; Practice Q5(b))
- I can explain why the value f(a) does not affect lim (x → a) f(x), using a graph with a hole and a separate dot. (Guide: Worked example 1(a); Practice Q1, Q5(c))
- I can explain why writing “= ∞” describes a limit that does not exist. (Guide: “A note on writing ∞”; Practice Q6(c))
Skills
- I can read left-hand and right-hand limits from a graph, including at a jump. (Guide: Worked example 1(b); Practice Q2, Q5(a))
- I can read a one-sided limit at an endpoint of the domain. (Guide: “One-sided and two-sided limits”; Practice Q5(d))
- I can recognise a jump, unbounded behaviour and oscillation on a graph, and name which one stops a limit existing. (Guide: “Three ways a limit can fail to exist”; Practice Q3, Q6(a))
- I can find x-values closer and closer to 0 where an oscillating function takes two different values. (Guide: Figure 2; Practice Q6(b))
- I can sketch a graph with open and filled circles that matches a list of limit statements. (Practice Q7(a))
Reasoning
- I can justify “the limit does not exist” by quoting the two one-sided limits, not just by saying “there is a jump”. (Practice Q5(b), Q7(b))
- I can explain how a graph’s scale or window can hide a hole or a narrow asymptote, and say how I would check. (Guide: Worked example 2; Practice Q4, Q7(d))
- I can say when my graph reading is only an estimate. (Guide: “What a graph tells you about a limit”)
All ticked? Move on to Estimating Limit Values from Tables, or return to the Calculus AB roadmap or the Calculus BC roadmap.