Proving Continuity of a Piecewise Function at x=1

[chaoseverlasting]

Homework Statement

f(x) is a piecewise function defined as:

$$2(2e-e^x) x<1$$
$$3\pi x-4 x>=1$$

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 $$3\pi -4$$. They seem to be equal, but how do I prove it mathematically? I've missed something here, but don't know what.

 

[Dick]

How many decimal places are you looking at? They aren't THAT close to being equal.

 

[chaoseverlasting]

No idea. Is this thing continuous at x=1?

 

[Dick]

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.

 

[chaoseverlasting]

Yeah, I did just that. The question has other parts which can only be solved if this thing was continuous. Nasty assumption.

 

[HallsofIvy]

2e and 3$\pi$-4 are definitely NOT equal!