Limits and Continuity - Intuitive Approach part 3

Limits and Continuity – Intutive Approach– Chapter 8 Paper 4: Quantitative Aptitude- Mathematics

Ms. Ritu Gupta B.A. (Hons.) Maths and MA (Maths)

Continuity

• Fundamental Knowledge • Its application

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Concept of Continuity

A function is said to be continuous at a point x = a if

(i) f(x) is defined at x = a

(ii)

(iii)

i.e. L.H.L = R.H.L = value of the function at x = a

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Discontinuous Function

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Properties of Continuous Functions

(i) If f(x) and g(x) are both continuous at a point x=a, then f(x)+g(x) is also continuous.

(ii) If f(x) and g(x) are both continuous at a point x=a then f(x) – g(x) is also continuous.

(iii) If f(x) and g(x) are both continuous at a point x=a then their product f(x) . g(x) is also continuous at x = a.

(iv) If f(x) and g(x) are both continuous at a point x=a then their quotient f(x)/ g(x) is also continuous at x=a and g(a) ≠ 0.

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Properties of Continuous Functions-Continued

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Illustrations

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Illustration 24

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Illustration 25

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Illustration 27

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Illustration 28

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Illustration 29

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Illustration 29 – Continued

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Illustration 30 A function f(x) is defined as follows:- f(x) = x2 when 0<x<1 = x when 1≤x<2 = (¼) x3 when 2≤x<3 Now f(x) is continuous at (a) x = 1 (b) x = 3 (c) x=0 (d) None of these Solution: Let us first check the continuity of a function f(x), at x = 1

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Illustration 30 - Continued

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Illustration 31

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Illustration 32

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Illustration 33

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Illustration 34

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Illustration 35

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Illustration 36

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Illustration 37

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Thank you

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