Eric Nicholas K's answer to Kathy's Secondary 4 A Maths Singapore question.
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Date Posted:
4 years ago
The modulus which the other tutor has put in the answer is not required in the O Levels but required in the A Levels.
The modulus sign is there to take into account the fact that 1/x is valid for all non-zero values of x, and therefore its integral should also be valid for negative x, but we know that the x in ln x cannot be negative, hence the modulus sign.
When we differentiate ln x, the x in ln x is in the first place only defined for x > 0, so its derivative x is also defined (at x > 0). Which is why you do not see any modulus at all during differentiation.
The modulus sign is there to take into account the fact that 1/x is valid for all non-zero values of x, and therefore its integral should also be valid for negative x, but we know that the x in ln x cannot be negative, hence the modulus sign.
When we differentiate ln x, the x in ln x is in the first place only defined for x > 0, so its derivative x is also defined (at x > 0). Which is why you do not see any modulus at all during differentiation.
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