sites.lafayette.edu/thompsmc/files/.../Section_14_4.pdf
Many functions that we study in calculus are quite difficult to deal with. However, in Calculus
1, we learned that if we are willing to introduce some error into our calculations with f(x), we can replace the original function with its ”linearization” at the point f(a). For example, consider the curve f(x) = sin(100/x):
If we are only interested in values for f(x) very close to, say x = 6.7, the line tangent to the curve looks very similar to the curve:
The more we zoom in, the harder it is to distinguish between f(x) and its ”linearization” atx = 6.5 (i.e. the tangent line at x = 6.5). Since the tangent line is a function that is much easierto work with, we can use the linearization near x = 6.5 to estimate values for f(x) near x = 6.5.
図 KidsがGrapesで描く。らしく描かれているが０近辺ではどうなのであろうか。
peda.com/gary/GrafEqApplications.pdf