Explain why ln(1 + x) = 1/2− x possible sol'n near 0; estimate w/ Taylor Polynomial!

[eagle2020]

Explain why ln(1 + x) = 1/2− x possible sol'n near 0; estimate w/ Taylor Polynomial!

Hi
I have trouble answering this question. Any help would be appreciated.

given the equation:
ln(1 + x) = 1/2− x
(a) Explain why the equation could have a solution for x close to 0.(b) Estimate the solution of the equation using the second-degree Taylor polynomial for ln(1+x).

Thanks for the help

 

[ksdhart2]

Given that you definitely read the Read Before Posting thread that's stickied a the top of each subforum, I'm assuming you've shared no work with us because you have none to share. That's fine. We can start at the very beginning.

For part (a), what does it mean for an equation to have a solution at some point? Does the given equation have a solution at x = 0? It asks about points "close to x = 0", so what about x = 0.5, x = 0.1, x = -0.1, etc? As you investigate, are you noticing any patterns that might help you answer the question?

For part (b), what is the definition of a Taylor polynomial? What does it mean for a Taylor polynomial to be second degree? Do you know how to create a Taylor polynomial? What do you get if you create the second degree Taylor polynomial for ln(1 + x)? How does that help you answer the question?