O-LevelAdditional MathematicsDifferentiation and integration4037/21 · May/June 2017 · Q34 Marks
The variables x and y are such that y = ln(x² + 1).
- (i)Find an expression for dy/dx[2]
- (ii)Hence, find the approximate change in y when x increases from 3 to 3 + h, where h is small.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.
- [B2] 2x / (x² + 1) final answer B1 for 1/(x²+1) × (ax+b), a or b must be non-zero
- [M1] dy ≈ (their (2x/(x²+1)))|_{x=3} × h or better Substitutes x = 3 into their dy/dx and multiplies by h
- [A1] 6/10 h oe
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