Since smaller nuclei have a larger surface area-to-volume ratio, the binding energy per nucleon due to the nuclear force generally increases with the size of the nucleus but approaches a limiting value corresponding to that of a nucleus with a diameter of about four nucleons.
42.
As the point " q " approaches " p ", which corresponds to making " h " smaller and smaller, the difference quotient should approach a certain limiting value " k ", which is the slope of the tangent line at the point " p ".
43.
If is any unit vector, the projection of the curl of onto is defined to be the limiting value of a closed line integral in a plane orthogonal to as the path used in the integral becomes infinitesimally close to the point, divided by the area enclosed.
44.
The first four methods are called "'directed rounding "', as the displacements from the original number " y " to the rounded value " q " are all directed towards or away from the same limiting value ( 0, + ", or " " ).
45.
While the above discussion has related to the convergence of a single series to a limiting value, the notion of the convergence of two series towards each other is also important, but this is easily handled by studying the sequence defined as either the difference or the ratio of the two series.
46.
The Bernoulli numbers can be expressed in terms of the Riemann zeta function as " " n? " ( 1 " " n " ) } } for integers provided for 0 } } and 1 } } the expression is understood as the limiting value and the convention } } is used.
47.
A physical interpretation of k can be given by observing that " k " is the limiting value of " Z " i as the size of the section ( in terms of values of its components, such as inductances, capacitances, etc . ) approaches zero, while keeping " k " at its initial value.
48.
One must be careful in this situation to correctly use the definition of eccentricity as the ratio of the distance of a point on the circle to the focus ( length of a radius ) to the distance of that point to the directrix ( this distance is infinite ) which gives the limiting value of zero.
49.
An example of an occurrence of the golden ratio is as the limiting value of the ratio of two successive Fibonacci numbers : even though the " n "-th such ratio is the ratio of two integers and hence is rational, the limit of the sequence of these ratios as " n " goes to infinity is the irrational golden ratio.
50.
Now I can appreciate the basic concept of what's going on here-as we take the limiting values of phi and the surface area for r \ to \ infty, phi tends to 0 sufficiently fast so that the integral over the surface tends to 0 despite the surface area becoming arbitrarily large, but what I want to know is "'why " '?
