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 name the two indeterminate forms 0/0 and ∞/∞ and explain why neither decides a limit. (Guide: “Limits that algebra cannot finish”; Practice Q5(a))
- I can explain why 0/0 is a label and not a value, so “= 0/0” must never appear in my working. (Guide: “Limits that algebra cannot finish”; Practice Q6(b))
- I can state L’Hospital’s Rule, including its conditions, and say that it uses f′(x)/g′(x), not the derivative of f(x)/g(x). (Guide: “The rule”; Practice Q6(b))
- I can explain with tangent lines why the ratio of the functions approaches the ratio of the slopes in a 0/0 limit. (Guide: “Why it works” and Figure 1)
Skills
- I can write a correct check that both limits are 0, or both infinite, before using the rule. (Guide: “How to write the justification”; Practice Q6(a))
- I can use the rule on a 0/0 limit with exponentials, logs or trig, using the chain rule. (Guide: Worked example 1; Practice Q1, Q6(a))
- I can use the rule on an ∞/∞ limit as x → ∞. (Guide: Worked example 2; Practice Q5(b))
- I can apply the rule more than once, checking the form each time. (Guide: Worked example 3; Practice Q4, Q5(b))
- I can find a limit from a table of f, g, f′ and g′ values at a point. (Guide: “Using a table of values”; Practice Q2)
Reasoning
- I can tell when the rule does not apply (nonzero/0, 0/∞, or a plain number) and say what the limit does instead. (Guide: “When not to use the rule”; Practice Q3, Q6(c))
- I can recognise when the rule loops and switch to algebra. (Guide: “When not to use the rule”)
- I can use a limit to choose a constant that makes a function continuous. (Practice Q7)
- I can interpret a limit of a ratio of two models in context. (Practice Q5(c))
All ticked? Move on to Topic 5.1, Using the Mean Value Theorem, or return to the Calculus AB roadmap or the Calculus BC roadmap.