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.

Sum

Solution

The limit of f(x) does not exist 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. (c) | Page 129

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:

x . log 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) = {{:(4x + 5",",  "if",  x ≤ 3),(4x - 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)`


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^3 + 64)/(x + 4), x_0` = – 4


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):}`


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.


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:

If f : R → R is defined by `f(x) = [x - 3] + |x - 4|` for x ∈ R then `lim_(x -> 3^-) f(x)` is equal to


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:

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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×