Home
Class 12
MATHS
For each x in R, let [x]be the greatest ...

For each `x in R`, let [x]be the greatest integer less than or equal to x. Then `lim_(xto0^-) (x([x]+absx)sin[x])/absx` is equal to a) -sin1 b) 0 c) 1 d) sin 1

A

`-2sin 1`

B

0

C

1

D

2sin 1

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • JEE 2019

    CENGAGE PUBLICATION|Exercise Chapter 3|5 Videos

  • JEE 2019

    CENGAGE PUBLICATION|Exercise Chapter 4|6 Videos

  • JEE 2019

    CENGAGE PUBLICATION|Exercise Chapter 1|5 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise All Questions|541 Videos

  • LIMITS

    CENGAGE PUBLICATION|Exercise Comprehension Type|4 Videos

Similar Questions

Explore conceptually related problems

let [x] denote the greatest integer less than or equal to x. Then lim_(xto0) (tan(pisin^2x)+(abs(x)-sin(x[x]))^2)/x^2

For each t in R ,let[t]be the greatest integer less than or equal to t. Then lim_(xto1^+)((1-absx+sinabs(1-x))sin(pi/2[1-x]))/(abs(1-x)[1-x])

For each tinR," let "[t] be the greatest integer less than or equal to t. Then find lim_(xto0^(+)) x([(1)/(x)]+[(2)/(x)]+...+[(15)/(x)])

Let [x] denotes the greatest integer less than or equal to x. If f(x) =[x sin pi x] , then f(x) is

If a and b are positive and [x] denotes greatest integer less than or equal to x, then find lim_(xto0^(+)) x/a[(b)/(x)].

Let [ x ] denote the greatest integer less than or equal to x, then the value of the integral int_-1^1 (absx - 2[x]) dx is equal to

Let [x] denote the greatest integer less than or equal to x, then the value of the integral int_(-1)^(1)(|x|-2[x])dx is equal to-

Let [x] denotes the greatest integer less then or equal to x. If x=(sqrt3+1)^5 , then [x] is equal to

lim_(xto0) (xcot(4x))/(sin^2x cot^2(2x)) is equal to

lim_(xto0) (sqrt(1-cos 2x))/(sqrt2x) is equal to-