Taylor polynomials for ln(x), based at x=1!
p_5:= x -> (x-1)-(x-1)^2/2+(x-1)^3/3-(x-1)^4/4+(x-1)^5/5;
Zio2I0kieEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLC45JCIiIiEiIkYrKiQsJkYqRitGLEYrIiIjI0YsRi8qJEYuIiIkI0YrRjIqJEYuIiIlI0YsRjUqJEYuIiImI0YrRjhGJUYlRiU=
plot([p_5(x), ln(x)], x=0..4, y=-10..10, color=[red, black]);
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
evalf(p_5(1/2)); evalf(p_5(2));
JCErbm1UJilvISM1
JCIrTExMTHkhIzU=
I can see from the graph that p_5(2) over-estimates ln(2).
However, how p_5(1/2) compares to ln(1/2) is too close for me to be able to tell with this interval, so I'll zoom in.
plot([p_5(x), ln(x)], x=.45.. .55, color=[red, black]);
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
I can see that the estimate is above the actual value, so P_5(1/2) is (barely) an over-estimate.
plot([abs(ln(x)-p_5(x)), .01], x=.45 .. 1.55, color=[red, blue]);
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