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 say which method fits a limit given as a graph, a table or a formula, and why a graph or table gives only an estimate. (Guide: “Step 1”; Practice Q7(c))
- I can explain what each result of substitution means: a number, nonzero over 0, or 0/0. (Guide: “Step 3” and Figure 1; Practice Q2, Q5)
- I can explain why f(a) does not decide lim (x → a) f(x), even for a piecewise function. (Guide: “Step 2”; Practice Q3, Q6(d))
Skills
- I can substitute first and stop when the result is a number with a nonzero bottom. (Guide: Worked example 1(i); Practice Q5(a))
- I can match a 0/0 form to factoring, a conjugate, combining fractions or an identity. (Guide: “Step 4”; Practice Q1, Q5(b))
- I can describe a nonzero-over-0 limit by checking the sign on each side. (Guide: Worked example 1(iii); Practice Q2, Q5(c))
- I can find one-sided limits for a piecewise function or an absolute value, and decide whether the two-sided limit exists. (Guide: Worked example 2; Practice Q3, Q7(b))
- I can find a constant that makes a piecewise limit exist. (Practice Q6(c))
- I can find the limit of a composite function from the inside out. (Guide: “Composite functions”; Practice Q4)
Reasoning
- I can name the procedure I chose and the reason for it before I calculate. (Guide: toolkit table; Practice Q5)
- I can find and correct a wrong choice of method in someone else’s working. (Practice Q7(a))
- I can recognise a limit, such as x cos(1/x) as x → 0, that needs the squeeze theorem rather than algebra. (Guide: “When none of these works”; Practice Q7(d))
All ticked? Move on to Topic 1.8, Determining Limits Using the Squeeze Theorem, or return to the Calculus AB roadmap or the Calculus BC roadmap.