Posted by paul on Monday, November 19, 2012 at 10:25pm.
assuming you want to use an "easily" calculatable value, let's approximate assuming we know the value of ln(1000).
the slope of the tangent at any point (x,y) on the curve is
m = 1/x
so, at x=1000, the slope is 1/1000.
Thus, we are using the line through (1000,ln1000) with slope 1/1000:
y = 1/1000 (x-1000) + ln1000
at x=1008,
y = 8/1000 + ln1000 = 6.915755
real value: 6.915723
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