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April 2, 2015

# Homework Help: calculus

Posted by paul on Monday, November 19, 2012 at 10:25pm.

Use the tangent line approximation to approximate the value of ln(1008)
• calculus - Steve, Tuesday, November 20, 2012 at 12:08am

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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