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Examine the continuity of f(x) = x3 + 2x2 − x − 2 at x = − 2

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प्रश्न

Examine the continuity of f(x) = x3 + 2x2 − x − 2 at x = − 2

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उत्तर

Every polynomial is continuous for all values of x f(x) = x3 + 2x2 − x − 2 is a polynomial and hence continuous at x = − 2.

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पाठ 8: Continuity - EXERCISE 8.1 [पृष्ठ १७२]

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संबंधित प्रश्‍न

Examine whether the function is continuous at the points indicated against them :

f(x) `{:(= x/(tan3x) + 2",",   "for"  x < 0),(= 7/3",",  "for"  x ≥ 0):}}  "at"  x = 0`


Test the continuity of the following function at the point or interval indicated against them :

f(x) `{:(= ((27 - 2x)^(1/3) - 3)/(9 - 3(243 + 5x)^(1/5))",",  "for"  x ≠ 0),(= 2",",  "for"  x = 0):}}` at x = 0.


Test the continuity of the following function at the point or interval indicated against them:

f(x) `{:( =(x^2 + 8x - 20)/(2x^2 - 9x + 10)",",  "for"  0 < x < 3","  x ≠ 2),(= 12",",  "for"  x = 2),(= (2 - 2x - x^2)/(x - 4)",",  "for"  3 ≤ x < 4):}}` at x = 2


Identify discontinuities for the following function as either a jump or a removable discontinuity :

f(x) = `(x^2 - 10x + 21)/(x - 7)`


Identify discontinuities for the following function as either a jump or a removable discontinuity :

f(x) `{:(= x^2 - 3x - 2",",  "for"  x < -3),(= 3 + 8x",",  "for"  x > -3):}`


Identify discontinuities for the following function as either a jump or a removable discontinuity :

f(x) `{:(= 4 + sin x",",  "for"  x < pi),(= 3 - cos x",",  "for"  x > pi):}`


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f(x) = `(x^2 - 1)/(x^3 + 1)` for x ≠ – 1


Discuss the continuity of the following function at the point indicated against them :

f(x) = `{:(=( sqrt(3) - tanx)/(pi - 3x)",", x ≠ pi/3),(= 3/4",", x = pi/3):}}  "at"  x = pi/3`


The following function has a removable discontinuity? If it has a removable discontinuity, redefine the function so that it become continuous :

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The following function has a removable discontinuity? If it has a removable discontinuity, redefine the function so that it become continuous :

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For what values of a and b is the function

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For what values of a and b is the function

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Show that there is a root for the equation 2x3 − x − 16 = 0 between 2 and 3.


Suppose f(x) `{:(= "p"x + 3",", "for"  "a" ≤ x ≤ "b"),(= 5x^2 − "q"",", "for"  "b" < x ≤ "c"):}`

Find the condition on p, q, so that f(x) is continuous on [a, c], by filling in the blanks.

f(b) = ______

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∴ pb + 3 = _______ − q

∴ p = `"_____"/"b"` is the required condition


Select the correct answer from the given alternatives:

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Discuss the continuity of the following function at the point(s) or on the interval indicated against them:

f(x) `{:(= (x^2 - 3x - 10)/(x - 5)",", "for"  3 ≤ x ≤ 6","  x ≠ 5),(= 10",", "for"  x = 5),(=(x^2 - 3x - 10)/(x - 5)",", "for"  6 < x ≤ 9):}`


Discuss the continuity of the following function at the point(s) or on the interval indicated against them:

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Identify discontinuity for the following function as either a jump or a removable discontinuity on their respective domain:

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Identify discontinuity for the following function as either a jump or a removable discontinuity on their respective domain:

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f(x) `{:(= "a"x^2 + "b"x + 1",", "for"  |2x - 3| ≥ 2),(= 3x + 2",", "for"  1/2 < x < 5/2):}`


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