The curve $C$ has equation $y = x^2 + \ln(2-x)$. Use a non-calculator method to find the equatio

Question

The curve $C$ has equation $y = x^2 + \ln(2-x)$. Use a non-calculator method to find the equation of the tangent to $C$ at the point where $x = 0$, leaving your answer in exact form.[3] Write down the coordinates of the point where the tangent meets $C$ again, correct to $3$ significant figures.[1] Sketch the graphs of $C$ and the tangent found in part (a) on a single diagram, stating the equations of any asymptotes and all the coordinates of the points of intersection with the axes.[4] Find the area of the finite region bounded by the curve $C$, the tangent and the line $x = 1$. Give your answer correct to $2$ decimal places.[2]

Accepted Answer

(a)$y=-\frac{1}{2}x+\ln 2$ (b)(1.99,-0.300) (d)0.28

2024 ASRJC H1 Q4

2024 ASRJC H1 Q4