# Tangents and Areas

Calculus Level pending

A tangent is drawn at a point $$P1$$ on the curve $$y=x^3$$.The tangent intersects the curve again at point $$P2$$. Another tangent is drawn at the point $$P2$$,it intersects the curve at $$P3$$ and so on.Prove that the $$abcissae$$ of the pts. $$P1, P2,...$$are in $$GP$$ and find the ratio: $$\dfrac{Area(\Delta (P1P2P3))}{Area(\Delta(P2P3P4)}$$

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