Calculus: Limits - Solving for Lim[f(x) + 2g(x)]

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Homework Help Overview

The discussion revolves around finding the limit of the expression f(x) + 2g(x) as x approaches positive infinity, given the limits of f(x) and g(x) at that point.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to substitute the known limits of f(x) and g(x) into the expression to find the limit. Other participants confirm the approach and express relief about their understanding.

Discussion Status

The discussion includes confirmations of the original poster's approach, with some participants expressing uncertainty about their correctness. There is a mention of basic properties of limits, which suggests a foundational understanding is being explored.

Contextual Notes

Participants reference a specific assignment context, indicating that the problem may be part of a structured homework task. There is a focus on ensuring the understanding of limit properties without resolving the discussion into a definitive conclusion.

Ris Valdez
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Homework Statement


Given that
lim f(x) = -4 and lim g(x) = 6
(All limits x --> +infinity)

Find the limit
lim [f(x) + 2g(x)]

Homework Equations



The Attempt at a Solution


So I substituted the values of f(x) and g(x) in the equation

=[(-4) + 2(6)
the limit is = 8

Did I do it right?
 
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Ris Valdez said:
Did I do it right?
Yep
 
Nathanael said:
Yep
Thanks! It was a wiley assignment and I thought I did it wrong xD
 
Ris Valdez said:
Thanks! It was a wiley assignment and I thought I did it wrong xD

What else could the limit possibly be?
 
PeroK said:
What else could the limit possibly be?
Sorry! I was just making sure.
 
You should know from basic properties of limits that
1) For any constant A, as long as lim f(x) exists, then so does lim Af(x) and the limit is A(lim f(x)).
2) As long as lim f(x) and lim g(x) exist, then so does lim f(x)+ g(x) and the limit is lim f(x)+ lim g(x).

Those two together give the result you want.
 

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