# How do you find the linear approximation of #f(x)=ln(x)# at #x=1# ?

##### 1 Answer

Here is the big key: The linear approximation of

#### Explanation:

The linear approximation of

The equation of the tangent line to the graph of

In point-slope form, the line is:

So we can write the tangent line as:

I struggled mightily with linear approximation for a week or two before this hit home and I realized that linear approximation is just a particular way of thinking about, writing, and using the tangent line. (My teacher had been saying it, I just didn't see it.)

**In this problem**

For

Therefore,

We also not that

The linear approximation is the line:

Or, simply

If you have a calculator of tables for

Note, however that