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Home > NCERT Solutions > Karnataka Board > Class 12 > Mathematics > Mathematics Part I > Chapter 5 Continuity And Differentiability

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TextBook Solutions for Karnataka Board Class 12 Mathematics Mathematics Part I Chapter 5 Continuity And Differentiability

Question 1

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Check the continuity of the function f given by f(x) = 2 x + 3 at x = 1.

Solution

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Question 2

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Prove that the function f(x) = 5 x – 3 is continuous at x = 0, at x = – 3 and at x = 5.

Easy

Question 3

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Examine the continuity of the function f(x) = 2x² –1 at.x = 3

Easy

Question 4

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Prove that the function f(x) = xⁿ is continuous at x = n, where n is a positive integer.

Easy

Question 5

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Examine whether the function f given by f(x) = x² is continuous at x = 0.

Easy

Question 6

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Is the function defined by f(x) = x² –sin x + 5 continuous at x = $WiredFaculty$ ?

Easy

Question 7

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Discuss the continuity of the function f given by f(x) = | x | at x = 0.

Average

Question 8

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Prove that the identity function on real numbers given by f(x) = x is continuous at every real number.

Easy

Question 9

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Show that the function defined by g(x) = x – [x] is discontinuous at all integral points. Here [x] denotes the greatest integer less than or equal to x

Easy

Question 10

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Find all the points of discontinuity of the greatest integer function defined by f(x) = [x], where [x] denotes the greatest integer less than or equal to x.

Easy

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