Answer Limit Question: -3 | Good Day

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Homework Help Overview

The discussion revolves around evaluating a limit involving exponential functions as the variable approaches negative infinity. The original poster expresses uncertainty about how to approach the problem despite knowing the answer.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants inquire if the original poster has attempted the limit evaluation. Suggestions include distributing terms and clarifying the relationship between different exponential expressions. There is also a question regarding the validity of an equation presented in a proof.

Discussion Status

The discussion includes various attempts to clarify the limit evaluation process. Some participants provide insights into the steps taken, while others express confusion about specific mathematical relationships. No explicit consensus has been reached, but there are multiple lines of reasoning being explored.

Contextual Notes

Participants are navigating through potential misunderstandings related to exponential functions and their behavior as the variable approaches negative infinity. There is a mention of a proof solution that may not align with the original poster's understanding.

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Good Day

I have this limit question that I need to evaluate. I know the answer but am unsure how to answer it.

Evalualte:

lim (3^(x+1))(2-3^(-x))
x-> -Infinity

I know the answer is -3.

Any help would be great
 
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have you tried it?
 
try distrubuting the [itex]3^{x+1}[/itex]
 
just looking the my proofs solution I don't understand how 3^(x+1) * 2 = 2e^(x+1). Can anybody explain this?
 
Mathnewbie said:
just looking the my proofs solution I don't understand how 3^(x+1) * 2 = 2e^(x+1). Can anybody explain this?

No, because they aren't equal.
 
i'm not sure what that is, but this is how i proved it:
[tex]\lim_{x\rightarrow -\infty} 3^{x+1} (2-3^{-x})[/tex]
[tex]\lim_{x\rightarrow -\infty} 2(3^{x+1}) - 3^{x+1-x}[/tex]
[tex]\lim_{x\rightarrow -\infty} 2(3^{x+1}) - 3[/tex]
where x approaches negative infinity, therefore, [itex]3^{-\infty} \rightarrow 0[/itex]
[tex]\lim_{x\rightarrow -\infty}3^{x+1} (2-3^{-x}) = - 3[/tex]
 

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