Differential Calculus
Differential Calculus
star_batch_jee_advanced_2025
Grade 12
Question:
Let $K > 0$ and $\lambda = \lim_{x \to 0} \frac{K\left(1-4\sqrt{K^2-x^2}\right)}{x^2\sqrt{K^2-x^2}}$ is finite then the value of $\lambda K$ is_____.
Step-by-Step Solution
Key Concept: Choose the substitution parameter so that the indeterminate form resolves to a finite non-zero limit.
Substitute $x = K \sin θ$ to transform the limit. For the limit to be finite as $θ \to 0$, we need $K = \frac{1}{4}$, which gives $λ = \frac{2}{K} = 8$.
Correct Answer: 0