Solving Trig Limit Question: Step-by-Step Guide

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Homework Help Overview

The problem involves evaluating the limit of the expression sin(x)/(x+tan(x)) as x approaches 0, which falls under the subject area of limits in calculus, particularly involving trigonometric functions.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of L'Hopital's rule as a potential method for solving the limit. There is also mention of the squeeze theorem as an alternative approach to evaluate the limit.

Discussion Status

Some participants have suggested specific methods such as L'Hopital's rule and the squeeze theorem, indicating a productive exploration of different approaches. However, there is no explicit consensus on the best method or final outcome yet.

Contextual Notes

There is an indication that the original poster has struggled with the problem and is seeking guidance on how to proceed, which suggests a need for clarification on the application of the proposed methods.

Mejiera
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Homework Statement



lim x appraoches 0 sin(x)/(x+tan(x))

Homework Equations



I have tryed everthing. Can someone show me how to do this.

The Attempt at a Solution

 
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Have you tried L'Hopital's rule?
 
Use L'Hopital's rule as Char suggested. The answer should come out to 1/2. If you have trouble applying the rule, let me know and i'll help you out.
 
Another way to see this: squeeze theorem with sin(x)/2tan(x) and sin(x)/2x.
 

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