Home
Class 12
MATHS
If : f(x){:( =1", ... x is ration...

If : `f(x){:( =1", ... x is rational"),(=0", ...x is irrational" ):}` then : `lim_(x to 0)f(x)=`

A

0

B

1

C

`1/2`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • LIMITS AND DERIVATIVES

    DISHA PUBLICATION|Exercise Exercise- 1 : Concept Builder (Topic 4)|15 Videos

  • JEE MAIN - 2019 (HELD ON: 9TH APRIL 2019(MORNING SHIFT))

    DISHA PUBLICATION|Exercise MCQs|30 Videos

  • LINEAR INEQUALITIES

    DISHA PUBLICATION|Exercise Exercise -2 : Concept Applicator|30 Videos

Similar Questions

Explore conceptually related problems

If f(x)={x^(2) if x is rational and 0, if x is irrational }, then

IF f(x)={{:(x,"if",x,"is rational"),(1-x,"if",x, "is irrational"):},"then find" lim_(xto1//2) f(x) if exists.

Knowledge Check

  • If f(x)={{:(1,"x is rational"),(2,"x is irrational"):} then

    A
    f(x) is continuous in `R~l`
    B
    f(x) is continuous in `R~Q`
    C
    f(x) is continuous in R but not differentiable in R
    D
    f(x) is neither continuous nor differentiable in R

  • Let f(x)={(1, "when x is rational"),(0, "when x is irrational'"):} then lim_(xrarr0) f(x) is :

    A
    0
    B
    1
    C
    `1/2`
    D
    none of these

  • If f(x)={(x",", "if x is rational "),(-x",","if x is irrational"):} , then

    A
    f(x) is an odd function
    B
    f(x) is continuous at `x=(1)/(2)`
    C
    f(x) is continuous at x = 0
    D
    f(x) is periodic function

    • Similar Questions

    Explore conceptually related problems

    f(x)={x if x is rational -x if x is irrational then Lt_(x rarr0)f(x)=

    Let f(x)={{:(x^(2),,"if x is rational"),(0,,"if x is irrational"):} then

    Let f(x) = [{:(x^(2), " if x is irrational"),(1, " if x is rational"):} , then

    Let f defined on [-5, 5] as f(x)={{:("x, if x is rational"),("-x, if x is irrational"):}, then f(x) is

    If F:[0,1] to [0,1]" be defined by "f(x)={{:(,x,"if x is rational"),(,1-x,"if x is irrational"):}, then (fof) x is:

    Home
    Profile