Before the midterm

Checking the limit but not the value

The habit: Continuity at a point needs the limit and the value to exist and to agree.

4 practice questions are built to catch it, in 1 topic.

See it fail in a figure: The value counts too, in the continuity lesson

What it looks like

A question from continuity, with the answer this slip gives beside the right one.

Standard2 marks · 4 min

The graph of a function $f$ is shown. Of $x = -3$ , $x = -1$ , $x = 1$ and $x = 3$ , which set lists exactly the ones at which $f$ is not continuous?

With the slip: $\displaystyle \{-3,\ -1\}$
Worked through: $\displaystyle \{-3,\ -1,\ 3\}$

At x = 3 the graph approaches the open circle at height 3 from both sides, so the limit exists, but the filled point puts f(3) = 5. A limit that exists is not enough: it must equal the value.

See the worked solution

Where it comes up

Continuity4 questions

Practise against it

Each of these has an answer this slip gives. Work them on paper: if you fall into it, the verdict names it and the question comes back in review.

Start the set