English
Tamil Nadu Board of Secondary EducationHSC Science Class 11

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

Advertisements
Advertisements

Question

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

Graph

Solution

The function f(x) is not defined at x = x0 and hence the continuity is destroyed at x = x0

shaalaa.com
Continuity
  Is there an error in this question or solution?
Chapter 9: Differential Calculus - Limits and Continuity - Exercise 9.5 [Page 129]

APPEARS IN

Samacheer Kalvi Mathematics - Volume 1 and 2 [English] Class 11 TN Board
Chapter 9 Differential Calculus - Limits and Continuity
Exercise 9.5 | Q 15. (b) | Page 129

RELATED QUESTIONS

Examine the continuity of the following:

x + sin x


Examine the continuity of the following:

e2x + x2


Examine the continuity of the following:

|x + 2| + |x – 1|


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


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

x0 = 1, `f(x) = {{:((x^2 - 1)/(x - 1)",", x ≠ 1),(2",", x = 1):}`


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?


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) = {{:((x - 1)^3",",  "if"  x < 0),((x + 1)^3",",  "if"  x ≥ 0):}`


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


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):}`


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 : R → R be defined by `f(x) = {{:(x, x  "is irrational"),(1 - x, x  "is rational"):}` then f is


Choose the correct alternative:

The function `f(x) = {{:((x^2 - 1)/(x^3 + 1), x ≠ - 1),("P", x = -1):}` is not defined for x = −1. The value of f(−1) so that the function extended by this value is continuous 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×