AS 91578 · 2024 paper · sec, graph, cone, triangle area
Question 3(b)(iii) Achieved
Practises Reading a graph: differentiability, f′ = 0, and limits
A product with sec, three readings off a drawn graph (continuity, stationary points, a limit), stationary points of a rational function, a related-rates cone, and an optimisation that has to be proved to a given exact value.
What is the value of limx → −1 f(x)? State clearly if the value does not exist.
Work it out
Try it on paper first. Stuck? Take one hint at a time.
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1 What height does the graph approach from each side of x = −1?
From the left, the line comes down towards 1. From the right, the curve rises away from 1. -
2 Does it matter that f(−1) itself is not defined?
No. A limit only asks where the graph is heading, and both sides head for 1.
What the marker wanted
- Achieved Two of the three answers to (i), (ii) and (iii) correct.
The schedule marks (i), (ii) and (iii) together as one Achieved item: any two of the three correct earns it.
In our words, from NZQA’s 2024 marking schedule.
How did it go?
Got it moves it further out. Review brings it back tomorrow.