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I am reading Bruce P. Palka's book: An Introduction to Complex Function Theory ...
I am focused on Chapter 4: Complex Integration, Section 1.2 Smooth and Piecewise Smooth Paths ...
I need help with some aspects of Example 1.3, Section 1.2, Chapter 4 ...
Example 1.3, Section 1.2, Chapter 4 reads as follows:View attachment 7419In the above text from Palka, we read the following:
"... ... Since $$\dot{ \gamma } ( 0 )$$ fails to exist, $$\gamma$$ is not smooth ... ... "I wish to rigorously demonstrate that $$\dot{ \gamma } ( 0 )$$ fails to exist ... but do not know how to proceed ...
Can someone please show me how to rigorously prove that $$\dot{ \gamma } ( 0 )$$ fails to existHelp will be much appreciated ...
Peter
I am focused on Chapter 4: Complex Integration, Section 1.2 Smooth and Piecewise Smooth Paths ...
I need help with some aspects of Example 1.3, Section 1.2, Chapter 4 ...
Example 1.3, Section 1.2, Chapter 4 reads as follows:View attachment 7419In the above text from Palka, we read the following:
"... ... Since $$\dot{ \gamma } ( 0 )$$ fails to exist, $$\gamma$$ is not smooth ... ... "I wish to rigorously demonstrate that $$\dot{ \gamma } ( 0 )$$ fails to exist ... but do not know how to proceed ...
Can someone please show me how to rigorously prove that $$\dot{ \gamma } ( 0 )$$ fails to existHelp will be much appreciated ...
Peter