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Unit 8: Continuity
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Thus we can say that if x and 2x are two continuous functions at x = a then (x + 2x) is also Notes
continuous at x = a.
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2
4. Consider the function f(x) = (x + 1)(x +2). We know that (x + 1) and (x + 2) are two
continuous functions.
Also f(x) = (x + 1)(x + 2)
2
3
3
= x + 2x + x + 2
3
As x , 2x , x and 2 are continuous functions, therefore.
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2
3
x + 2x + x + 2 is also a continuous function.
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We can say that if (x + 1) and (x + 2) are two continuous functions then (x + 1)(x + 2) is also
2
a continuous function.
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5. Consider the function f(x) = at x = 2. We know that (x – 4) is continuous at x = 2. Also
(x + 2) is continuous at x = 2.
Again =
=
= 2 – 2 = 0
Also f(2) =
= = 0
f(x) = f(2). Thus f(x) is continuous at x = 2.
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If (x – 4) and x + 2 are two continuous functions at x = 2, then is also continuous.
6. Consider the function f(x) =|x – 2|. The function can be written as:
f(x) =
=
=
= 2 – 2 = 0
=
…(i)
=
= 2 – 2 = 0 …(ii)
Also f(2) = (2 – 2) = 0 …(iii)
From (i), (ii) and (iii),
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