Tangent at a point \( P_{1}\{ \) other than \( (0,0)\} \) on the curve \( y= \) \( x^{3} \) meet...
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Tangent at a point \( P_{1}\{ \) other than \( (0,0)\} \) on the curve \( y= \) \( x^{3} \) meets the curve again at \( P_{2} \). The tangent at \( P_{2} \) meets the curve at \( P_{3} \) and so on.
Show that the abacissa of \( P_{1}, P_{2}, P_{3}, \ldots ., P_{n} \), form a GP. Also, find the ratio of \( \left[\operatorname{area}\left(\Delta P_{1} P_{2} P_{3}\right)\right] /\left[\operatorname{area}\left(\Delta P_{2} P_{3} P_{4}\right)\right] \).
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