Find the equation of the tangent line (Can someone check my work?)

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Discussion Overview

The discussion revolves around finding the equation of the tangent line to the function g(x) = arctan(x) + ln(x) at the point x = 1. Participants evaluate a proposed solution and discuss the importance of showing work in mathematical problems.

Discussion Character

  • Homework-related, Debate/contested

Main Points Raised

  • One participant presents the equation of the tangent line as $$y - \frac{\pi}{4} = \frac{3}{2}(x - 1)$$ and claims it is correct.
  • Another participant agrees with the solution but emphasizes the lack of shown work, suggesting that verification of the derivative g'(x) and the formula for the tangent line is necessary.
  • A later reply reiterates the importance of showing work, indicating that without it, potential errors in the solution cannot be identified.

Areas of Agreement / Disagreement

While some participants agree that the proposed answer is correct, there is a consensus on the necessity of demonstrating the work leading to that answer. The discussion remains unresolved regarding the verification of the solution due to the absence of supporting calculations.

Contextual Notes

Limitations include the lack of detailed steps in the original post, which prevents verification of the correctness of the solution and the understanding of the underlying concepts.

shamieh
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Find the equation of the tangent line to g(x) = arctan(x) + ln(x) @ x = 1

$$y - \frac{\pi}{4} = \frac{3}{2}(x - 1)$$
 
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Looks good to me. :D
 
shamieh said:
Find the equation of the tangent line to g(x) = arctan(x) + ln(x) @ x = 1

$$y - \frac{\pi}{4} = \frac{3}{2}(x - 1)$$

Your answer is indeed correct, but as no actual work is shown, we cannot verify that you didn't just happen to "guess" the right answer (although you probably didn't).

Things a teacher might want to see included in your answer:

1) What is g'(x)?

2) What is the formula for the tangent line to g(x) at x = a?

The correct two answers to the questions I have listed above are actually more important than "the final answer".
 
Deveno said:
Your answer is indeed correct, but as no actual work is shown...

This is an excellent point. If you answer happened to be incorrect, we would not have been able to address where you made any errors.
 

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