PYQ Vault
EbooksTutor

Number of points where a greatest integer function is not continuous and not differentiable (m + n)

This type of question, asked 2 times: 14 Jun 2022, 10 Apr 2023. All 2 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    14 Jun 2022

    155
    Let f(x)={sin⁡(x−[x])x−[x],x∈(−2,−1)max{2x,3[∣x∣]},∣x∣<11, otherwise f(x) =\left\{ \begin{matrix} \frac{\sin(x - \lbrack x\rbrack)}{x - \lbrack x\rbrack} & , & x \in ( - 2, - 1) \\ \mathbf{max\{ 2x,3\lbrack|x|\rbrack\}} & , & |x| < 1 \\ 1, & & \text{~otherwise~} \end{matrix} \right. where [t]\lbrack t\rbrack denotes greatest integer ≤t\leq t. If mm is the number of points where ff is not continuous and nn is the number of points where ff is not differentiable, then the ordered pair (m,n)(m,n) is :

    Tap an option to check your answer.

  2. Question 2

    10 Apr 2023

    82
    Let f:(−2,2)→f:( - 2,2) \rightarrow IR be defined by
    f(x)={x[x],−2<x<0(x−1)[x],0≤x<2f(x) =\left\{ \begin{matrix} x\lbrack x\rbrack & , - 2 < x < 0 \\ (x - 1)\lbrack x\rbrack & ,0 \leq x < 2 \end{matrix} \right.
    Where [x]\lbrack x\rbrack denotes the greatest integer function. If mm and nn respectively are the number of points in (−2,2)( - 2,2) at which y=∣f(x)∣y = |f(x)| is not continuous and not differentiable, then m+nm + n is equal to