How do you use the tangent line approximation to approximate the value of $ln (1004)$ $ln(1004)$ ?

Question

How do you use the tangent line approximation to approximate the value of $ln (1004)$ $ln(1004)$ ?

1 Answer

Impact of this question

5710 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2014-10-28T21:12:06

A formula for a tangent line approximation of a function f, also called linear approximation , is given by

$f(x)~~f(a)+f'(a)(x-a),$
which is a good approximation for $x$ when it is close enough to $a$ .

I'm not sure, but I think the question is about approximate the value $ln(1.004)$ . Could you verify it please? Otherwise we will need to know an approximation to $ln(10).$

In this case, we have $f(x)=ln(x)$ , $x=1.004$ and $a=1$ .

Since,
$f'(x)=1/x=>f'(1)=1$ and $ln(1)=0$ , we get

$ln(1.004)~~ln(1)+1*(1.004-1)=0.004.$

Science

Math

Humanities

... and beyond

How do you use the tangent line approximation to approximate the value of $ln (1004)$ $ln(1004)$ ?

1 Answer

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you use the tangent line approximation to approximate the value of ln(1004)ln(1004)ln(1004) ?

1 Answer

Related questions

Impact of this question

How do you use the tangent line approximation to approximate the value of $ln (1004)$ $ln(1004)$ ?