First order term in the taylor expansion of ln(x) abut 1

[Mr Davis 97]

Homework Statement

What's the first order term in the expansion ln(x) about x = 1?

Homework Equations

Taylor series formula

The Attempt at a Solution

The question is multiple choice, and the choices are x, 2x, or (1/2)x. However, when I calculate the first order term in the expansion of ln(x) about 1, I get ln(1) + (1/1)(x - 1) = x - 1, which is not one of the options. What am I doing wrong?

 

[SammyS]

Homework Statement

What's the first order term in the expansion ln(x) about x = 1?

Homework Equations

Taylor series formula

The Attempt at a Solution

The question is multiple choice, and the choices are x, 2x, or (1/2)x. However, when I calculate the first order term in the expansion of ln(x) about 1, I get ln(1) + (1/1)(x - 1) = x - 1, which is not one of the options. What am I doing wrong?

So, what's the first order term in x - 1 ?

 

[Mr Davis 97]

x... But how is that the answer if x - 1 is the first order term in the Taylor approximation?

 

[vela]

The question is multiple choice, and the choices are x, 2x, or (1/2)x. However, when I calculate the first order term in the expansion of ln(x) about 1, I get ln(1) + (1/1)(x - 1) = x - 1, which is not one of the options. What am I doing wrong?

Nothing. The problem statement is wrong or, at best, misleading. My guess is the intent was to ask what the linear term of ln(1+x) about x=0 is.