Question

The angle at which the curve y = ke^kx intersects the y- axis is

• A. tan^–1(k²)
• B. cot^–1 (k²)
• C. sin^–1 (1/$\sqrt{1 + k^{4}}$)
• D. sec^–1$\sqrt{1 + k^{4}}$

Answer 1

Answer: (B)

cot^–1 (k²)

Answer 2

$\frac{dy}{dx}$= k² e^kx. The curve intersects y- axis at (0, k) so $\left. \ \frac{dy}{dx} \right|_{(0,k)}$

= k². If θ is the angle at which the given curve intersects the y- axis then tan (π/2 – θ) =$\frac{k^{2} - 0}{1 + 0.k^{2}}$= k².

Hence θ = cot^–1 k²