# Limit homework problem help

1. Mar 1, 2007

### chaoseverlasting

1. The problem statement, all variables and given/known data
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.

2. Relevant equations

3. 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.

2. Mar 1, 2007

### Dick

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

3. Mar 1, 2007

### chaoseverlasting

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

4. Mar 1, 2007

### Dick

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: Mar 1, 2007
5. Mar 4, 2007

### chaoseverlasting

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

6. Mar 5, 2007

### HallsofIvy

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