Theorem of continuity and limits converge

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Homework Help Overview

The discussion revolves around theorems of continuity and limits, specifically focusing on the limits of the functions f(x) and g(x) as x approaches a. The original poster presents a problem involving the limits of the sum and difference of these functions and seeks to find the limit of their product.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to apply theorems of continuity to derive values for f(a) and g(a) based on the given limits. Some participants question the initial steps taken and suggest methods for solving the resulting equations.

Discussion Status

The discussion is progressing with participants providing guidance on how to manipulate the equations derived from the limits. There is an indication that the original poster has made some progress in understanding the relationships between the functions.

Contextual Notes

The original poster expresses uncertainty about their initial approach and seeks clarification on the next steps. There is an emphasis on using theorems of continuity to establish relationships between the functions at the point a.

Satyr
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Homework Statement


If lim x--> a of [f(x) + g(x)]=2 and lim x--> a of [f(x) - g(x)] = 1, then find lim x--> a f(x)g(x)


Homework Equations


Theorems of continuity


The Attempt at a Solution


Since I'm not quite sure if what I began with was right, it didn't yield me any type of a valid answer. But from the theorems of continuity (lim x--> a of f(x)=f(a)), I began with saying lim x-->2 of [f(x)+g(x)]=2 and lim x-->1 of [f(x)-g(x)]=1

is that a good place to start? where do I go from here?
thanks
 
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You mean continuity of f and g tells you f(a)+g(a)=2 and f(a)-g(a)=1, right? That's two equations in two unknowns. You should be able to solve for f(a) and g(a).
 
right, I've figured that part
i was wondering where I begin doing that?

thanks
 
Add the two equations together to get an equation for just f(a).
 

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