English
Tamil Nadu Board of Secondary EducationHSC Science Class 11

Choose the correct alternative: Let a function f be defined by f(x)=x-|x|x for x ≠ 0 and f(0) = 2. Then f is - Mathematics

Advertisements
Advertisements

Question

Choose the correct alternative:

Let a function f be defined by `f(x) = (x - |x|)/x` for x ≠ 0 and f(0) = 2. Then f is

Options

  • Continuous nowhere

  • Continuous everywhere

  • Continuous for all x except x = 1

  • Continuous for all x except x = 0

MCQ

Solution

Continuous for all x except x = 0

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 25 | Page 131

RELATED QUESTIONS

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


Examine the continuity of the following:

x2 cos x


Examine the continuity of the following:

`sinx/x^2`


Examine the continuity of the following:

|x + 2| + |x – 1|


Find the points of discontinuity of the function f, where `f(x) = {{:(sinx",",  0 ≤ x ≤ pi/4),(cos x",", pi/4 < x < pi/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):}`


Show that the function `{{:((x^3 - 1)/(x - 1)",",  "if"  x ≠ 1),(3",",  "if"  x = 1):}` is continuous om `(- oo, oo)`


Let `f(x) = {{:(0",",  "if"  x < 0),(x^2",",  "if"  0 ≤ x ≤ 2),(4",",  "if"  x ≥ 2):}`. Graph the function. Show that f(x) continuous on `(- oo, oo)`


Find the points at which f is discontinuous. At which of these points f is continuous from the right, from the left, or neither? Sketch the graph of f.

`f(x) = {{:(2x + 1",",  "if"  x ≤ - 1),(3x",",  "if"  - 1 < x < 1),(2x - 1",",  "if"  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?


Which of the following functions f has a removable discontinuity at x = x0? If the discontinuity is removable, find a function g that agrees with f for x ≠ x0 and is continuous on R.

`f(x) = (x^2 - 2x - 8)/(x + 2), x_0` = – 2


Which of the following functions f has a removable discontinuity at x = x0? If the discontinuity is removable, find a function g that agrees with f for x ≠ x0 and is continuous on R.

`f(x) = (3 - sqrt(x))/(9 - x), x_0` = 9


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


The function `f(x) = (x^2 - 1)/(x^3 - 1)` is not defined at x = 1. What value must we give f(1) inorder to make f(x) continuous at x =1?


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×