NCERT Solutions for Class 12 Term_policy Mathematics Part I Chapter 5 Continuity And Differentiability

Continuity And Differentiability Here is the CBSE Term_policy Chapter 5 for Class 12 students. Summary and detailed explanation of the lesson, including the definitions of difficult words. All of the exercises and questions and answers from the lesson's back end have been completed. NCERT Solutions for Class 12 Term_policy Continuity And Differentiability Chapter 5 NCERT Solutions for Class 12 Term_policy Continuity And Differentiability Chapter 5 The following is a summary in Hindi and English for the academic year 2025-26. You can save these solutions to your computer or use the Class 12 Term_policy.

Question 1

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

Solution

Here space space space space space space space space space space space space space space space space space space space space space space space straight f left parenthesis straight x right parenthesis equals 2 straight x plus 3 Lt with straight x rightwards arrow 1 below space straight f left parenthesis straight x right parenthesis equals Lt with straight x rightwards arrow 1 below space left parenthesis 2 straight x plus 3 right parenthesis equals 2 left parenthesis 1 right parenthesis plus 3 equals 2 plus 3 equals 5 Now space straight f space is space defined space at space straight x equals 1 and space space straight f left parenthesis 1 right parenthesis equals 2 left parenthesis 1 right parenthesis plus 3 equals 2 plus 3 equals 5 therefore stack Lt space with straight x rightwards arrow 1 below space straight f left parenthesis straight x right parenthesis equals straight f left parenthesis 1 right parenthesis equals 5 therefore space straight f space is space continous space at space straight x equals 1.

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NCERT Solutions for Class 12 Term_policy 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

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For Daily Free Study Material Join wiredfaculty

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NCERT Solutions for Class 12 Term_policy 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 =?