Question

Tangent at a point P₁ {other than (0, 0)} on the curve y = x³ meets the curve again at P₂. The tangent at P₂ meets the curve at P₃, and so on. Show that the abscissa of P₁, P₂, P₃,. ..., P_n, form a GP. Also find the ratio [area(Δ P₁ P₂ P₃)]/[area(P₂ P₃ P₄)]

Answer 1

On putting the value of y in Eq. (i)

Therefore, x = -2h is the point P₂,

Hence, the abscissa are h, -2h, 4h, -8h,... which form a GP.