Lakshesh Verma Lakshesh Verma

Lecture 1 : Continuity & Differentiability of a Function; Concept of Infinity & Algebra of Continuous Functions

  • Chapter-5. Continuity and Differentiability Assignments 1

     

    Find all the points of discontinuity of f defined by.

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  • Chapter-5. Continuity and Differentiability Assignments 2


    Examine that  is a continuous function.

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  • Chapter-5. Continuity and Differentiability Assignments 3

    Show that the function defined by is a continuous function.

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  • Chapter-5. Continuity and Differentiability Assignments 4

     

    Show that the function defined by f (x) = cos (x2) is a continuous function.

     

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  • Chapter-5. Continuity and Differentiability Assignments 5

     

    Find the values of aand b such that the function defined by

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  • Chapter-5. Continuity and Differentiability Assignments 6

     

    Find the values of k so that the function fis continuous at the indicated point.

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  • Chapter-5. Continuity and Differentiability Assignments 7

    Find the values of k so that the function fis continuous at the indicated point.

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  • Chapter-5. Continuity and Differentiability Assignments 8

     

    Find the values of k so that the function fis continuous at the indicated point.

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  • Chapter-5. Continuity and Differentiability Assignments 9

     

    Find the values of k so that the function fis continuous at the indicated point.

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  • Chapter-5. Continuity and Differentiability Assignments 10

     

    Examine the continuity of f, where f is defined by

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  • Chapter-5. Continuity and Differentiability Assignments 11

      

    Determine if fdefined by

    is a continuous function?

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  • Chapter-5. Continuity and Differentiability Assignments 12

      

    Find the points of discontinuity of f, where

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  • Chapter-5. Continuity and Differentiability Assignments 13

    Discuss the continuity of the cosine, cosecant, secant and cotangent functions,

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  • Chapter-5. Continuity and Differentiability Assignments 14

      

    Discuss the continuity of the following functions.

    (a) f(x) = sin x + cos x

    (b) f(x) = sin x - cos x

    (c) f(x) = sin x x cos x

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  • Chapter-5. Continuity and Differentiability Assignments 15

    Is the function defined by continuous at x = π?

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  • Chapter-5. Continuity and Differentiability Assignments 16

    Show that the function defined by is discontinuous at all integral point. Here denotes the greatest integer less than or equal to x.

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  • Chapter-5. Continuity and Differentiability Assignments 17

     

    For what value of is the function defined by

    continuous at x = 0? What about continuity at x= 1?

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  • Chapter-5. Continuity and Differentiability Assignments 18

     

    Find the relationship between aand b so that the function fdefined by

    is continuous at x = 3.

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  • Chapter-5. Continuity and Differentiability Assignments 19

      

    Discuss the continuity of the function f, where f is defined by

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  • Chapter-5. Continuity and Differentiability Assignments 20

      

    Discuss the continuity of the function f, where f is defined by

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  • Chapter-5. Continuity and Differentiability Assignments 21

     

    Discuss the continuity of the function f, where f is defined by

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  • Chapter-5. Continuity and Differentiability Assignments 22

     

    Is the function defined by

    a continuous function?

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  • Chapter-5. Continuity and Differentiability Assignments 23

     

    Find all points of discontinuity of f, where f is defined by

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  • Chapter-5. Continuity and Differentiability Assignments 24

     

    Find all points of discontinuity of f, where f is defined by

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  • Chapter-5. Continuity and Differentiability Assignments 25

     

    Find all points of discontinuity of f, where f is defined by

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  • Chapter-5. Continuity and Differentiability Assignments 26

     

    Find all points of discontinuity of f, where f is defined by

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  • Chapter-5. Continuity and Differentiability Assignments 27

     

    Find all points of discontinuity of f, where f is defined by

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  • Chapter-5. Continuity and Differentiability Assignments 28

     

    Find all points of discontinuity of f, where f is defined by

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  • Chapter-5. Continuity and Differentiability Assignments 29

     

    Is the function fdefined by

    continuous at x= 0? At x= 1? At x= 2?

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  • Chapter-5. Continuity and Differentiability Assignments 30

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

     

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  • Chapter-5. Continuity and Differentiability Assignments 31

    Examine the continuity of the function.

     

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  • Chapter-5. Continuity and Differentiability Assignments 32

    Prove that the functionis continuous at

     

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    • Description:-

    Lecture 1:
    Today, we will discuss the first three topics, i.e; Continuity & Differentiability of a Function; Concept of Infinity & Algebra of Continuous Functions respectively of Chapter 5 Continuity and Differentiability.
    Objectives:
    1. Basic concept about Continuity & Differentiability of a Function.
    2. Concept of Infinity.
    3. Concept of Algebra of Continuous Functions.
    Important Tip: 
    This lecture is about Continuity & Differentiability of a Function; Concept of Infinity & Algebra of Continuous Functions. In this topic, you’ll get to learn all about Continuity & Differentiability. You'll also get to know about the Infinity and Algebra of Continuous function. Have a clear focus on these topics as it help you in further studies also.
    Please go through the topic, their notes. Properly do the assignments, watch videos of the concerned topics. If you have any doubt about any topic/point please submit it in the discussion section... it will be answered as soon as possible.
    After all of this... when you feel confident about the particular topic/chapter then take the quiz.

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