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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 - Mathematics

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प्रश्न

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

पर्याय

  • Continuous nowhere

  • Continuous everywhere

  • Continuous for all x except x = 1

  • Continuous for all x except x = 0

MCQ
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उत्तर

Continuous for all x except x = 0

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Continuity
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 9: Differential Calculus - Limits and Continuity - Exercise 9.6 [पृष्ठ १३१]

APPEARS IN

सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 11 TN Board
पाठ 9 Differential Calculus - Limits and Continuity
Exercise 9.6 | Q 25 | पृष्ठ १३१

संबंधित प्रश्‍न

Examine the continuity of the following:

x + sin x


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x . log x


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


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|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 + 2",",  "if",  x ≥ 2),(x^2",",  "if",  x < 2):}`


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 = 3, `f(x) = {{:((x^2 - 9)/(x - 3)",", "if"  x ≠ 3),(5",", "if"  x = 3):}`


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) = (x^3 + 64)/(x + 4), x_0` = – 4


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.


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


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