Figure 1. 4: The graph shows the successive asmptotic approximations to the Note

Question

Figure 1. 4: The graph shows the successive asmptotic approximations to the Note that in figure 1. 4, the curves y = 1 and y = 1 - x + 2x2 cross at x = 1/2, the curves y = 1 - x and y = 1-x+2x2-6x3 cross at x = 1 /3. and the curves y = 1 - x + 2x2 and 1 - x + 2x2 -6x3 + 24x4 cross at x = 1/4. Show that the pattern continues. That is, show that the nth degree polynomial approximation and the (n - 2)nd degree polynomial approximation cross at x = 1/n. Note that in figure 1. 4, the curves y = 1 andy = 1 - x + 2x2 cross at x = 1/2, the curves y = 1 - x and y = 1-x+2s2-6x3 cross at x - 1 /3. and the curves y = 1 - x + 2x2 and 1 - x + 2x2 -6x3 + 24x4 cross at x = 1/4. Show that the pattern continues. That is, show that the nth degree polynomial approximation and the (n - 2)nd degree polynomial approximation cross at x = 1/n.

Explanation / Answer

The given property of the given Integral function S(x) has been shown in the text.. The values that follow them are 1/8, 1/16, so on. It is the basic property of an integral function.

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