Let $$f\left( x \right) = \left[ {{x^3} - 3} \right],\,\left[ x \right] = {\text{G}}{\text{.I}}{\text{.F}}{\text{.}}$$ Then the number of points in the interval $$\left( {1,\,2} \right)$$ where function is discontinuous is :
A.
5
B.
4
C.
6
D.
3
Answer :
6
Solution :
$$\eqalign{
& f\left( x \right) = \left[ {{x^3} - 3} \right] \cr
& {\left( {1.26} \right)^3} = 2 - 3 = - 1\,;\,{\left( {1.44} \right)^3} = 3 - 3 = 0 \cr} $$
Similarly, we can check for other points where $$f\left( x \right)$$ changes values to $$1,\,2,\,3,\,4$$
$$\therefore $$ Total number of points of discontinuity are '6'
Releted MCQ Question on Calculus >> Continuity
Releted Question 1
For a real number $$y,$$ let $$\left[ y \right]$$ denotes the greatest integer less
than or equal to $$y:$$ Then the function $$f\left( x \right) = \frac{{\tan \left( {\pi \left[ {x - \pi } \right]} \right)}}{{1 + {{\left[ x \right]}^2}}}$$ is-
A.
discontinuous at some $$x$$
B.
continuous at all $$x,$$ but the derivative $$f'\left( x \right)$$ does not exist for some $$x$$
C.
$$f'\left( x \right)$$ exists for all $$x,$$ but the second derivative $$f'\left( x \right)$$ does not exist for some $$x$$
The function $$f\left( x \right) = \frac{{\ln \left( {1 + ax} \right) - \ln \left( {1 - bx} \right)}}{x}$$ is not defined at $$x = 0.$$ The value which should be assigned to $$f$$ at $$x = 0,$$ so that it is continuous at $$x =0,$$ is-
The function $$f\left( x \right) = \left[ x \right]\cos \left( {\frac{{2x - 1}}{2}} \right)\pi ,\,\left[ . \right]$$ denotes the greatest integer function, is discontinuous at-
The function $$f\left( x \right) = {\left[ x \right]^2} - \left[ {{x^2}} \right]$$ (where $$\left[ y \right]$$ is the greatest integer less than or equal to $$y$$ ), is discontinuous at-