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Home > NCERT Solutions > Punjab School Education Board > Class 12 > Mathematics > Mathematics Part I > Chapter 5 Continuity And Differentiability

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TextBook Solutions for Punjab School Education 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.

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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.

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Question 3

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

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Question 4

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

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Question 5

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

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Question 6

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

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Question 7

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

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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.

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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

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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.

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TextBook Solutions for Punjab School Education Board Class 12 Mathematics Mathematics Part I Chapter 5 Continuity And Differentiability

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

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

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

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

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

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

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

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

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

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.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

For Daily Free Study Material Join wiredfaculty

WhatsApp Group

Download Android App

Ncert Book Download

TextBook Solutions for Punjab School Education Board Class 12 Mathematics Mathematics Part I Chapter 5 Continuity And Differentiability

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

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

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

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

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

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

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

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

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

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.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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

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

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

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