Home
Class 11
MATHS
Prove that lim(x->3^+) x/[[x]] != lim(x...

Prove that `lim_(x->3^+) x/[[x]] != lim_(x->3^-) x/([x])` ( where [ ] is greatest integer function )

Text Solution

Verified by Experts

Given, `lim_(xto3^(+))x/([x])= lim_(hto0)((3+h))/([3+h])`
`lim_(hto0)(3+h)/(3)=1`
Promotional Banner

Topper's Solved these Questions

  • LIMITS AND DERIVATIVES

    NCERT EXEMPLAR|Exercise OBJECTIVE TYPE QUESTIONS|23 Videos

  • INTRODUCTION TO THREE DIMENSIONAL GEOMETRY

    NCERT EXEMPLAR|Exercise Fillers|16 Videos

  • LINEAR INEQUALITIES

    NCERT EXEMPLAR|Exercise Objective Type Questions|14 Videos

Similar Questions

Explore conceptually related problems

lim_(x rarr0^(-))([x])/(x) (where [.] denotes greatest integer function) is

lim_(x rarr1^(-1))([x])^(1-x) where [.] denotes greatest integer function

lim_(x -> 0)[sin[x-3]/([x-3])] where [.] denotes greatest integer function is

lim_(x rarr2)(-1)^([x]), where [x] is the greatest integer function,is equal to

lim_(x rarr2)(-1)^([x]), where [x] is the greatest integer function,is equal to

lim_(xrarr oo) (logx)/([x]) , where [.] denotes the greatest integer function, is

lim_(x->oo)[x^2/(sinxtanx)],where [.] denotes greatest integer function.

lim_(x rarr-1)([x]+|x|). (where [.] denotes the greatest integer function)

lim_(xrarr0) x^8[(1)/(x^3)] , where [.] ,denotes the greatest integer function is