How does f(x) = [x] behave at x = 5/2?

Continuity & Differentiability · Question 9 of 125

Question 9

EasyOriginal question

How does $f(x) = [x]$ behave at $x = \frac{5}{2}$ ?

Not continuous: the left and right limits differCorrect answerYour answerContinuous at the pointCorrect answerYour answerNot continuous: the limit exists but differs from the valueCorrect answerYour answerNot continuous: the function has no value thereCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

On $(2, 3)$ , $[x] = 2$ : $f$ is constant near $\frac{5}{2}$ .
Both one-sided limits and $f\left(\frac{5}{2}\right)$ equal 2: continuous.

Worth noting

$[x]$ jumps only at integers, and $\frac{5}{2}$ is not one.

Concept: Testing continuity at a point
Typical timeTypical: 60 s
Your timeYours: —

The rule this testsContinuity at a point

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How does f(x)=[x]f(x) = [x]f(x)=[x] behave at x=52x = \frac{5}{2}x=25​?

Explanation

How does $f(x) = [x]$ behave at $x = \frac{5}{2}$ ?