Moreover, the area of the region between the secant line and the quartic below the secant line equals the area of the region between the secant line and the quartic above the secant line.
32.
Moreover, the area of the region between the secant line and the quartic below the secant line equals the area of the region between the secant line and the quartic above the secant line.
33.
If too large, the calculation of the slope of the secant line will be more accurately calculated, but the estimate of the slope of the tangent by using the secant could be worse.
34.
Letting and be the distinct inflection points of a quartic, and letting be the intersection of the inflection secant line and the quartic, nearer to than to, then divides into the golden section:
35.
In this case the first-order errors cancel, so the slope of these secant lines differ from the slope of the tangent line by an amount that is approximately proportional to h ^ 2.
36.
This power equals the product of distances from "'P "'to any two intersection points of the circle with a secant line passing through "'P " '.
37.
This is entirely analogous to the construction of the tangent to a curve as a limit of the secant lines through pairs of distinct points on " C " approaching " P ".
38.
If the first term in this series is the area of the triangle, then the second is the sum of the areas of two triangles whose bases are the two smaller secant lines, and so on.
39.
Those standard parallels may be visualized as secant lines where the cone intersects the globe or, if the map maker chooses the same parallel twice, as the tangent line where the cone is tangent to the globe.
40.
Jensen's inequality generalizes the statement that the secant line of a convex function lies " above " the graph of the function, which is Jensen's inequality for two points : the secant line consists of weighted means of the convex function,
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