Limit homework problem help

  • #1

Homework Statement


f(x) is a piecewise function defined as:

[tex]2(2e-e^x) x<1[/tex]
[tex]3\pi x-4 x>=1[/tex]

Discuss the continuity of f(x) at x=1.


Homework Equations





The Attempt at a Solution



Putting x=1 in the above function gives you 2e and [tex]3\pi -4[/tex]. They seem to be equal, but how do I prove it mathematically? I've missed something here, but dont know what.
 

Answers and Replies

  • #2
Dick
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How many decimal places are you looking at? They aren't THAT close to being equal.
 
  • #3
No idea. Is this thing continuous at x=1?
 
  • #4
Dick
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No idea. Is this thing continuous at x=1?
It's a lot easier to show they aren't equal than that they are. Hint: they can't be equal, e and pi are algebraically independent. Just punch the things into calculator that shows more than two decimal places.
 
Last edited:
  • #5
Yeah, I did just that. The question has other parts which can only be solved if this thing was continuous. Nasty assumption.
 
  • #6
HallsofIvy
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2e and 3[itex]\pi[/itex]-4 are definitely NOT equal!
 

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