The function H(x) defined by

Find the conditions on that make

1. Continuous at

2. Differentiable at

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- Mar 30th 2008, 05:38 AMglioDifferentiating a function with a Heaviside Step Function
The function H(x) defined by

Find the conditions on that make

1. Continuous at

2. Differentiable at - Mar 30th 2008, 10:10 AMroy_zhang
1. In order to make continuous at , the function needs to satisfy the following conditions:

(1) is defined;

(2) exists; and

(3)

To satisfy (1), consider , we need is defined.

To satisfy (2), we need to make sure both and exist, also .

Here we have and .

So we need and .

To satisfy (3), realize that from above, if exists then . Also we have , hence .

In summary, in order to make continuous at , function has to satisfy .

2. Given that , so in order to make differentiable at , we need to show the limit exists. More specifically, we need to show the one-sided limits and exist and are equal. Can you pick up from here?

Roy - Mar 30th 2008, 10:46 AMglio
Thanks man.

I finally have ideas how to appreach this (Clapping)

Hmmm... It looks like I'll need more help with this.