Tuesday, September 30, 2008
Mandatory Quiz -- Thursday, Oct 2
Will focus on Chapter 2 (limits, continuity, derivatives (calculation via the definition)).
Chapter 2, section 8
Someone asked a question after class about the derivative of the absolute value. Here's a little more verbage for clarification:
The derivative of f(x)=|x| at any point to the right of 0 is 1 (eg., the slope of the line is 1). The derivative of |x| to the left of 0 is -1. So the derivative f'(x) is a piecewise function. (This is what I forgot to write down.) It is
{ 1, x >= 0
{ -1, x < 0
So as we found, the limit of f'(x) does not exit at 0 (left and right hand limits are not equal). But this is made more clear by the jump from -1 to 1 in the graph of f'(x).
-Jesse
The derivative of f(x)=|x| at any point to the right of 0 is 1 (eg., the slope of the line is 1). The derivative of |x| to the left of 0 is -1. So the derivative f'(x) is a piecewise function. (This is what I forgot to write down.) It is
{ 1, x >= 0
{ -1, x < 0
So as we found, the limit of f'(x) does not exit at 0 (left and right hand limits are not equal). But this is made more clear by the jump from -1 to 1 in the graph of f'(x).
-Jesse
Monday, September 29, 2008
Thursday, September 18, 2008
Monday, September 8, 2008
Chapter 2, section 2
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