At how many points in the open interval $(0, 2)$ is $f(x) = [2x]$ not continuous?

1

Correct answerYour answer

2

Correct answerYour answer

3

Correct answerYour answer

4

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

$[2x]$ jumps when $2x$ is an integer, that is at $x = \frac{1}{2}, 1, \frac{3}{2}$ inside $(0, 2)$ .
3 points.

Worth noting

1 counts only the integer $x = 1$ ; the factor 2 doubles how often it jumps.

Ten questions from Continuity & Differentiability, at your own pace.

Ten questions from Continuity & Differentiability, at your own pace.

At how many points in the open interval (0,2)(0, 2)(0,2) is f(x)=[2x]f(x) = [2x]f(x)=[2x] not continuous?