The curve ${{C}_{1}}$ and ${{C}_{2}}$ have equations $y=\frac{x}{{{x}^{2}}+1}$ and \(y=\sqrt{\

Question

The curve ${{C}_{1}}$ and ${{C}_{2}}$ have equations $y=\frac{x}{{{x}^{2}}+1}$ and $y=\sqrt{\frac{5}{4}-{{x}^{2}}}$ respectively. Sketch ${{C}_{1}}$ and ${{C}_{2}}$ on the same diagram, stating the exact coordinates of any points of intersection with the axes and stationary points, the equation(s) of any asymptote(s).[4] State the coordinates of the point of intersection of ${{C}_{1}}$ and ${{C}_{2}}$.[1] Hence solve the inequality $\frac{x}{{{x}^{2}}+1}\ge \sqrt{\frac{5}{4}-{{x}^{2}}}$.[1]

Accepted Answer

(ii) $\left( 1,\frac{1}{2} \right)$ (iii) $1 \le x \le \frac{\sqrt{5}}{2}$

2021 NYJC Promo Q6

2021 NYJC Promo Q6

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