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Prove that the lim x→3   3x+4=13  using the formal definition of a limit.

 Feb 5, 2019

Best Answer 

 #2
avatar+6251 
+2

ϵ>0 show δ|x3|<δ|3x+413|<ϵ

 

|3x+413|<ϵ|3x9|<ϵϵ<3x9<ϵ9ϵ<3x<9+ϵ3ϵ3<x<3+ϵ3|x3|<ϵ3

 

so choose δ=ϵ3and working everything backwards you end up with|3x+413|<ϵas desired

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 Feb 5, 2019
 #1
avatar+80 
+1

Can't you just plug in the value 3 for x?

 

What do you mean by formal definition of a limit?

 Feb 5, 2019
 #3
avatar+322 
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I wish it was that easy

Ruublrr  Feb 6, 2019
 #2
avatar+6251 
+2
Best Answer

ϵ>0 show δ|x3|<δ|3x+413|<ϵ

 

|3x+413|<ϵ|3x9|<ϵϵ<3x9<ϵ9ϵ<3x<9+ϵ3ϵ3<x<3+ϵ3|x3|<ϵ3

 

so choose δ=ϵ3and working everything backwards you end up with|3x+413|<ϵas desired

Rom Feb 5, 2019
 #4
avatar+118696 
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I'm sure you are correct Rom but I am with itsyaboi.

Talking about needing to go the long way around!

Melody  Feb 6, 2019
 #5
avatar+6251 
+1

well he did ask to use the formal definition of a limit  cheeky

Rom  Feb 6, 2019
 #6
avatar+118696 
0

Yes i understand that.    laugh

Sometimes I think mathematicians (not you) purposely design things to be complicated when it does not seem remotely necessary. 

Melody  Feb 6, 2019

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