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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 left-hand limit and right–hand limit does not coincide at x = x 

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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. (d) | पृष्ठ १२९

संबंधित प्रश्‍न

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


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 - 16)/(x + 4)`


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):}`


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):}`


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) = {{:((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


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.


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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


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


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