The function f(x)=[sinx] is not continuous at ([x] is the greatest integer less than or equal to x)

# The function f(x)=[sinx] is not continuous at ([x] is the greatest integer less than or equal to x)

1. A
$\frac{\pi }{2}$
2. B
$\pi$
3. C
$\frac{3\pi }{2}$
4. D

5. E
2$\pi$

Fill Out the Form for Expert Academic Guidance!l

+91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)

I agree to the terms and conditions and privacy policy.

### Solution:

We know f(x)=[x] is discontinuous at integral values of x.
Then, f(x)=[sinx] will be discontinuous where sinx will be integer.
Thus the solution set is, sinx=0,±1x=nπ,(2n+1)$\frac{\pi }{2}$​, where nI
Hence 1 is the correct option.

## Related content

 Area of Square Area of Isosceles Triangle Pythagoras Theorem Triangle Formula Perimeter of Triangle Formula Area Formulae Volume of Cone Formula Matrices and Determinants_mathematics Critical Points Solved Examples Type of relations_mathematics

Talk to our academic expert!

+91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)

I agree to the terms and conditions and privacy policy.