O-LevelAdditional MathematicsDifferentiation and integration4037/21 · May/June 2019 · Q25 Marks
Two variables x and y are such that y = In x / x³ for x > 0.
- (i)Show that dy/dx = (1 - 3 ln x) / x⁴.[3]
- (ii)Hence find the approximate change in y as x increases from e to e + h, where h is small.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.
- [B1] d/dx (ln x) = 1/x soi
- [M1] x³(1/x) - 3x² ln x / (x³)² or x⁻³(1/x) + (-3x⁻⁴)ln x
- [A1] Completion to given answer: dy/dx = (1 - 3 ln x) / x⁴
- [M1] (1 - 3 ln e) / e⁴ * h
- [A1] -2h/e⁴ oe or -0.0366h awrt
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