Q. 74.3( 3 Votes )

# Discuss the continuity of f(x) = [x].

Let n be any integer

[x] = Greatest integer less than or equal to x.

Some values of [x] for specific values of x

[3] = 3

[4.4] = 4

[-1.6] = -2

Therefore,

Left hand limit at x = n

= = n – 1

Right hand limit at x = n

= = n

Also, f(n) = [n] = n

As

Therefore, f(x) = [x] is discontinuous at x = n.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Super 10 Question: Check Your Knowledge of Maxima & Minima (Quiz)45 mins
Maxima & Minima in an interval60 mins
Questions Based on Maxima & Minima57 mins
Questions based on Maxima & Minima in an interval59 mins
Check your Knowlege of Maxima & Minima ( Challenging Quiz)60 mins
Connection B/w Continuity & Differentiability59 mins
Problems Based on L-Hospital Rule (Quiz)0 mins
When does a Maxima or Minima occur?48 mins
Interactive Quiz on Limits67 mins
Differentiability by using first principle59 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses