Tag: continuity

Number of points of discontinuity of $f\left( x \right) = \left[ {2{x^3} - 5} \right]$ in $\left[ {1,2} \right)$ is where $\left[ x \right]$ denotes greatest integer function are

$f(x)=\displaystyle\lim _{n\rightarrow \infty}\dfrac{(x-1)^{2n}-1}{(x-1)^{2n}+1}$ is discontinuous at

If $f\left( x \right) ={ \left( \tan { \left( \dfrac { \pi  }{ 4 } +\ell nx \right)  }  \right)  }^{ \log _{ x }{ e }  }$ is to be made continuous at $X=1$, then $f(1)$ should be equal to

The function $f\left( x \right)=\left[ x \right] \cos { \left( \pi \left( \dfrac { 2x-1 }{ 2 }  \right)  \right)  } $. (where [.] denotes the greatest integer function ) is discontinuous.  

If $f(x)=\dfrac {1}{x^{2}-17x+66}$ then $f\left(\dfrac {2}{x-2}\right)$ is discontinuous at $x=$

The sum of all values of $x$ for which $f(x)=[3\sin x]$ is discontinous in $[0,\ 2\pi]$ is (where [.] represents greatest integers function)

Consider the function defined on $[0,\ 1]\rightarrow R,\ f(x)=\dfrac {\sin x-x\cos x}{x^{2}}$ if $x\neq 0$ and $f(0)=0$ then the function of $f(x)$. 

The function $f(x)={ sin }^{ -1 }(cosx)$ is :

If $f\left( x \right) =\begin{cases} -1,if\ x<0\ \ 0,if\ x=0\ \ 1,if\ x>0\ \end{cases}$ and $g\left(x\right)=\sin x +\cos x$, then point discontinuity of $(fog)(x)$ in $(0,2\pi)$ are 

$f(x)=\min { \left{ x,{ x }^{ 2 } \right} ,\forall x\epsilon R } $ then $f(x)$ is