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Question
If f.g is continuous at x = a, then f and g are separately continuous at x = a.
Options
True
False
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Solution
This statement is False.
Explanation:
Let us take an example: f(x) = sin x and g(x) = cot x
∴ f(x).g(x) = sinx . cotx
= `sin x * cosx/sinx`
= = cos x
Which is continuous at x = 0 but cot x is not continuous at x = 0.
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