English
Tamil Nadu Board of Secondary EducationHSC Science Class 11

Choose the correct alternative: The value of klimx→kx-[x], where k is an integer is - Mathematics

Advertisements
Advertisements

Question

Choose the correct alternative:

The value of `lim_(x -> "k") x - [x]`, where k is an integer is

Options

  • – 1

  • 1

  • 0

  • 2

MCQ

Solution

1

shaalaa.com
Continuity
  Is there an error in this question or solution?
Chapter 9: Differential Calculus - Limits and Continuity - Exercise 9.6 [Page 131]

APPEARS IN

Samacheer Kalvi Mathematics - Volume 1 and 2 [English] Class 11 TN Board
Chapter 9 Differential Calculus - Limits and Continuity
Exercise 9.6 | Q 20 | Page 131

RELATED QUESTIONS

Prove that f(x) = 2x2 + 3x - 5 is continuous at all points in R


Examine the continuity of the following:

x + sin x


Examine the continuity of the following:

`sinx/x^2`


Examine the continuity of the following:

cot x + tan x


Find the points of discontinuity of the function f, where `f(x) = {{:(4x + 5",",  "if",  x ≤ 3),(4x - 5",",  "if",  x > 3):}`


Find the points of discontinuity of the function f, where `f(x) = {{:(x^3 - 3",",  "if"  x ≤ 2),(x^2 + 1",",  "if"  x < 2):}`


At the given point x0 discover whether the given function is continuous or discontinuous citing the reasons for your answer:

x0 = 3, `f(x) = {{:((x^2 - 9)/(x - 3)",", "if"  x ≠ 3),(5",", "if"  x = 3):}`


For what value of `alpha` is this function `f(x) = {{:((x^4 - 1)/(x - 1)",",  "if"  x ≠ 1),(alpha",",  "if"  x = 1):}` continuous at x = 1?


A function f is defined as follows:

`f(x) = {{:(0,  "for"  x < 0;),(x,  "for"  0 ≤ x ≤ 1;),(- x^2 +4x - 2, "for"  1 ≤ x ≤ 3;),(4 - x,  "for"  x ≥ 3):}`
Is the function continuous?


Find the constant b that makes g continuous on `(- oo, oo)`.

`g(x) = {{:(x^2 - "b"^2,"if"  x < 4),("b"x + 20,  "if"  x ≥ 4):}`


Consider the function  `f(x) = x sin  pi/x`. What value must we give f(0) in order to make the function continuous everywhere?


State how continuity is destroyed at x = x0 for the following graphs.


State how continuity is destroyed at x = x0 for the following graphs.


State how continuity is destroyed at x = x0 for the following graphs.


Choose the correct alternative:

Let the function f be defined by `f(x) = {{:(3x, 0 ≤ x ≤ 1),(-3 + 5, 1 < x ≤ 2):}`, then


Choose the correct alternative:

At x = `3/2` the function f(x) = `|2x - 3|/(2x - 3)` is


Choose the correct alternative:

Let f be a continuous function on [2, 5]. If f takes only rational values for all x and f(3) = 12, then f(4.5) is equal to


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×