The discussion revolves around finding the first order term in the Taylor expansion of the natural logarithm function, ln(x), about the point x = 1. Participants are exploring the implications of the Taylor series formula in this context.
Some participants express confusion regarding the discrepancy between their calculations and the provided options. There is a suggestion that the problem statement may be misleading, with a proposal to consider an alternative interpretation involving ln(1+x) instead.
Participants note that the problem is presented as a multiple choice question, which may influence their approach and understanding. There is an indication that the original problem statement might not align with standard expectations for the Taylor expansion of ln(x) about x = 1.
So, what's the first order term in x - 1 ?Mr Davis 97 said: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?
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.Mr Davis 97 said: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?