Thursday

August 21, 2014

August 21, 2014

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

- calculus -
**Steve**, Tuesday, November 20, 2012 at 12:08amassuming 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

**Related Questions**

Calculus - Use linear approximation, i.e. the tangent line, to approximate 8.4^(...

Calculus - Use linear approximation, i.e. the tangent line, to approximate 8.4...

ap calculus ab - for f(x)=lnx we know that f(e)=1. Use the tangent line at(e,1) ...

calculus - Let f be the function given by f(x)= x^2+4x-8. The tangent line to ...

Calculus - Use linear approximation, i.e. the tangent line, to approximate (1/0....

Math - Use linear approximation, i.e. the tangent line, to approximate 1.6^3 as ...

calculus - Use differentials (or equivalently, a linear approximation) to ...

math - Use the tangent line approximation to approximate the value of ln(1.004)

Calculus - Find the linear approximation of the function f(x)=^3sqrt(1+3x) at a=...

Math - Use linear approximation, i.e. the tangent line, to approximate sqrt[3...