Draft:Bpow41

Look at the graph of <m>y = x^n</m>, with n > 1, in the first quadrant. Let P the point on the graph at distance s from the origin and Q the point with coordinates (s,0). The line through P and Q intesects the y-axis at some point (0,T). What is the limit of T as s goes to zero?

For the more adventurous: Investigate what happens with other functions, f(x), satisfying the conditions that f(0) = 0, f '(0) = 0. What appears to be the general behaviour?

For the really adventurous: In the description above, take P to be the point at distance s from the origin measured in arclength along the graph. Now what is the limit?

Problem by Alberto L Delgado, from the now extinct Bradley Problem of the Week.