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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 = 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. (a) | पृष्ठ १२९

संबंधित प्रश्‍न

Examine the continuity of the following:

e2x + x2


Examine the continuity of the following:

x . log x


Examine the continuity of the following:

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


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):}`


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):}`


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)`


If f and g are continuous functions with f(3) = 5 and `lim_(x -> 3) [2f(x) - g(x)]` = 4, find g(3)


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):}`


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:

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:

The value of `lim_(x -> "k") x - [x]`, where k is an integer is


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 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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