The tangent to the curve $y=2\ln(x+1)$ at $A$, where $x=3$, meets the $y$-axis at $B$

Question

The tangent to the curve $y=2\ln(x+1)$ at $A$, where $x=3$, meets the $y$-axis at $B$. Find the equation of the tangent at $A$.[3] Hence find the exact area enclosed by the curve, the tangent and the $y$-axis.[5]

Accepted Answer

(i) $y=\dfrac{x}{2}-\dfrac32+2\ln4$ (ii) $\dfrac{15}{4}-2\ln4\text{ units}^2$

Logarithmic curve and its tangent beside the y-axis

Logarithmic curve and its tangent beside the y-axis

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