Problem of the Week

 

PROBLEM CC The sketch on the left shows the graph of the function f (x) = xn. At the point (a,f (a)) draw the tangent line, shown in red, and the line perpendicular to this tangent line,  shown in green.  Label the y-intercept of this last line P(a).  What is   ? For the lion-hearted:  Find a necessary and sufficient condition for this limit to exist and be non-zero.

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ã2004 Alberto L. Delgado