TS EAMCET · Maths · Application of Derivatives
If \(x=t-\sin t, y=1-\cos t\) and \(\frac{d^2 y}{d x^2}=-1\) at \(t=\mathrm{K}, \mathrm{K}>0\), then \(\underset{t \rightarrow \mathrm{~K}}{\operatorname{Lt}} \frac{y}{x}=\)
- A \(\frac{2}{\pi}\)
- B \(\frac{\pi-2}{2}\)
- C \(\frac{2}{\pi-2}\)
- D \(\frac{\pi}{2}\)
Answer & Solution
Correct Answer
(C) \(\frac{2}{\pi-2}\)
Step-by-step Solution
Detailed explanation
\(\frac{dy}{dx} = \frac{dy/dt}{dx/dt} = \frac{\sin t}{1-\cos t} = \frac{2\sin(t/2)\cos(t/2)}{2\sin^2(t/2)} = \cot(t/2)\)…
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