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October 25, 2014

October 25, 2014

Posted by **Jake** on Sunday, January 8, 2012 at 4:43pm.

- ap calculus ab -
**Steve**, Sunday, January 8, 2012 at 5:54pmf'(x) = 1/x

so, at (e,1), the slope is 1/e

the line is thus

(y-1)/(x-e) = 1/e

y = 1/e (x-e) + 1

y = x/e

at x=3, the line has y-value

y = 3/e

y = 1.104

Actual value of ln3 = 1.099

Since the curve is concave down, it will lie below the tangent line, so any linear approximation using just the tangent line will be too high.

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