# Limit homework problem help

## 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.

## 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 dont know what.

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

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

Dick
Homework Helper
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.

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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!