Therefore, we have shown the limit of the "secant parabolas" to be

(6)        .  

Therefore, the "tangent parabola" in (5) is revealed to be the Taylor polynomial of degree .  

Exploration 2.

The previous limits can be used to find the limit of the secant polynomials.

This is the answer we seek,

        ,  
        
but Mathematica had its preferred way of writing the answer.  If you need to verify that it is correct, then Mathematica can do it.

Of course, we could take each limit individually, then there would be no confusion.

(c) John H. Mathews 2004