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

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प्रश्न

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

आलेख

उत्तर

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

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Continuity
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 9: Differential Calculus - Limits and Continuity - Exercise 9.5 [पृष्ठ १२९]

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सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 11 TN Board
पाठ 9 Differential Calculus - Limits and Continuity
Exercise 9.5 | Q 15. (b) | पृष्ठ १२९

संबंधित प्रश्‍न

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


Examine the continuity of the following:

ex tan x


Examine the continuity of the following:

e2x + x2


Examine the continuity of the following:

`sinx/x^2`


Examine the continuity of the following:

`(x^2 - 16)/(x + 4)`


Examine the continuity of the following:

cot x + tan x


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 = 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^3 + 64)/(x + 4), x_0` = – 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.


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 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


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