Let [x] be the greatest integer function...

Let [x] be the greatest integer function `f(x)=(sin(1/4(pi[x]))/([x]))` is

Not continuous at any point

Continuous at 3/2

Discontinuous at 2

Differentiable at 4/3

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

CONTINUITY AND DIFFERENTIABILITY
ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|26 Videos
CONTINUITY AND DIFFERENTIABILITY
ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|11 Videos
CONTINUITY AND DIFFERENTIABILITY
ARIHANT MATHS|Exercise Exercise For Session 7|10 Videos
COMPLEX NUMBERS
ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|43 Videos
COORDINATE SYSTEM AND COORDINATES
ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

Similar Questions

Explore conceptually related problems

Find the period of the functions (where [ * ] denotes greatest integer function) f(x) = sin"" (pi x)/(4) + sin""(pi x)/(3)

Let f(x)=sin x,g(x)=[x+1] and h(x)=gof(x) where [.] the greatest integer function. Then h'((pi)/(2)) is

Let [.] represent the greatest integer function and f(x)=[tan^(2)x] then :

Sketch the graph of the following function: (i) f(x)=[Ix-1].] denotes the greatest integer function (ii) f(x)=x+[x.] denotes the greatest integer function.? eli- f(x)=sin|?[x].[.] denotes the greatest integer function.2

If f(x)=e^(sin(x-[x])cospix) , where [x] denotes the greatest integer function, then f(x) is

The greatest value of function f(x)=(sin(2x))/(sin(x+(pi)/(4)))

Let f(x) = (sin (pi [ x + pi]))/(1+[x]^(2)) where [] denotes the greatest integer function then f(x) is

Let f(x) = (sin (pi [ x - pi]))/(1+[x^2]) where [] denotes the greatest integer function then f(x) is

ARIHANT MATHS-CONTINUITY AND DIFFERENTIABILITY-Exercise (Single Option Correct Type Questions)

Consider function f: R - {-1,1}-> R. f(x)=x/[1-|x|] Then the incorrect...
Text Solution
|
If the functions f : R -> R and g : R -> R are such that f(x) is conti...
Text Solution
|
The total number of points of non-differentiability of f(x) = min[|sin...
Text Solution
|
The function f(x)=[x]^2-[x^2] is discontinuous at (where [gamma] is t...
Text Solution
|
The function f(x) = (x^(2) - 1)|x^(2)-6x + 5|+cos|x| is not differenti...
Text Solution
|
If f(x) = {{:((1)/(e^(1//x))",",x ne 0),(0",",x = 0):} then
Text Solution
|
Given f(x) = (e^(x)-cos 2x - x)/(x^(2)),"for x" in R-{0} g(x) = {{:(f(...
Text Solution
|
The function g(x) = {{:(x+b",",x lt 0),(cos x",",x ge 0):} cannot be m...
Text Solution
|
The graph of function f contains the point P(1, 2) and Q(s, r). The e...
Text Solution
|
Consider f(x)=[(2(sinx-sinx-sin^3x))+|sinx-sin^3 x|)/(2(sinx-sin^3 x)...
Text Solution
|
If f(x+y) = f(x) + f(y) + |x|y+xy^(2),AA x, y in R and f'(0) = 0, then
Text Solution
|
Let f(x) = max. {|x^2 - 2 |x||,|x|} and g(x) = min. {|x^2 - 2|x||, |x|...
Text Solution
|
Let g(x)=[(3x^2-4sqrtx+1, x<1),(ax+b, x>=1)) If g(x) is continuous and...
Text Solution
|
Let f(x) be continuous and differentiable function for all reals and f...
Text Solution
|
Let [x] be the greatest integer function f(x)=(sin(1/4(pi[x]))/([x])) ...
Text Solution
|
If f(x) = {{:(b([x]^(2)+[x])+1",","for",x ge -1),(sin(pi(x+a))",","for...
Text Solution
|
If both f(x) & g(x) are differentiable functions at x=x0then the fun...
Text Solution
|
Number of points of non-differentiability of the function g(x) = [x^2...
Text Solution
|
If f(x) = ({x}g(x))/({x}g(x)) is a periodic function with period (1)/(...
Text Solution
|
If f((x)/(y))=(f(x))/(f(y)) for all x, y in R, y ne 0 and f'(x) exists...
Text Solution
|