The curve $C$ has equation $y = \ln(5-2x^2)$. Sketch the graph of $C$, stating the equations o

Question

The curve $C$ has equation $y = \ln(5-2x^2)$. Sketch the graph of $C$, stating the equations of the asymptotes and the coordinates of the points of intersection with the axes.[3] Use a non-calculator method to find the equation of the tangent to $C$ at the point where $x = \sqrt{2}$, giving your answer in the form $y = ax + b$, where $a$ and $b$ are exact constants to be found.[3] Find the area of the finite region bounded by the curve $C$, its tangent at $x = \sqrt{2}$ and the $y$-axis. Give your answer correct to $3$ significant figures.[2]

Accepted Answer

(a) Asymptotes $x=\pm\sqrt{\frac52}$; intercepts $(\pm\sqrt2,0)$, $(0,\ln5)$. See sketch. (b) $y=-4\sqrt2x+8$. (c) $3.92$ units$^2$.

2024 CJC H1 Q4

2024 CJC H1 Q4

Solution:

Solution locked