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## Homework Statement

Prove, using the formal definition of limits:

If [PLAIN]http://rogercortesi.com/eqn/tempimagedir/eqn4201.png [Broken] and c>0, then [PLAIN]http://rogercortesi.com/eqn/tempimagedir/eqn4201.png [Broken] [Broken] (add the constant beside f(x) here, I couldn't get the equation generator to cooperate)

## Homework Equations

## The Attempt at a Solution

My text proved one kind of similar, so using that I get this:

Since [PLAIN]http://rogercortesi.com/eqn/tempimagedir/eqn4201.png [Broken] [Broken] for e/|c| > 0,

there exists a d > 0 such that

|cf(x) + c*inf| < e/|c| for 0 < |x-inf|< d

Hence,

|cf(x) + c*inf| = |c||f(x) + inf| < e/|c|*|c| = e for 0< |x-inf|< d.

I'm probably way out to lunch here... what do the pros think?

Thanks,

Jim

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