LFD Book Forum Problem 3.5
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#1
07-26-2014, 04:07 PM
 BojanVujatovic Member Join Date: Jan 2013 Posts: 13
Problem 3.5

I have questions about this problem. What I get after analyzing is the following:

The last line follows because:
(since )

From this, I cannot see how is not continuous at . Instead I find that it is not continuous nor differentiable for 's such that .

Any help would be greatly appreciated.
#2
07-30-2014, 08:39 AM
 magdon RPI Join Date: Aug 2009 Location: Troy, NY, USA. Posts: 597
Re: Problem 3.5

There are 3 cases:

in which case , which is differentiable.

in which case , which is differentiable.

in which case , but is not differentiable because the derivative is 0 or not depending on whether approaches 1 from above or below.

Quote:
 Originally Posted by BojanVujatovic I have questions about this problem. What I get after analyzing is the following: The last line follows because: (since ) From this, I cannot see how is not continuous at . Instead I find that it is not continuous nor differentiable for 's such that . Any help would be greatly appreciated.
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#3
08-03-2014, 09:23 PM
 BojanVujatovic Member Join Date: Jan 2013 Posts: 13
Re: Problem 3.5

The only part I don't quite follow is:
Quote:
 Originally Posted by magdon in which case , which is differentiable.
As I see, and please correct me if I'm wrong, for , the signal and the output agree.
(e.g. and ).

Therefore, and , meaning also .

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