Math Amateur
Gold Member
MHB
- 3,920
- 48
I am reading the book: Multivariable Mathematics by Theodore Shifrin ... and am focused on Section 3.1 Partial Derivatives and Directional Derivatives ...
I need some help with Example 3 in Chapter 3, Section 1 ...
Example 3 in Chapter 3, Section 1 reads as follows:View attachment 8587In the above text we read the following:" ... ... $$\lim_{ t \to 0 } \frac{ \| a + t \frac{a}{ \| a \| } \| - \| a \| }{ t } = \lim_{ t \to 0 } \frac{ ( \| a \| - t ) - \| a \| }{ t } $$ ... ... "
Can someone please explain exactly how $$\lim_{ t \to 0 } \frac{ \| a + t \frac{a}{ \| a \| } \| - \| a \| }{ t } = \lim_{ t \to 0 } \frac{ ( \| a \| - t ) - \| a \| }{ t } $$ ... ... ... indeed, specifically how $$\| a + t \frac{a}{ \| a \| } \| = ( \| a \| - t )$$ ... ...
Help will be appreciated ...
Peter
I need some help with Example 3 in Chapter 3, Section 1 ...
Example 3 in Chapter 3, Section 1 reads as follows:View attachment 8587In the above text we read the following:" ... ... $$\lim_{ t \to 0 } \frac{ \| a + t \frac{a}{ \| a \| } \| - \| a \| }{ t } = \lim_{ t \to 0 } \frac{ ( \| a \| - t ) - \| a \| }{ t } $$ ... ... "
Can someone please explain exactly how $$\lim_{ t \to 0 } \frac{ \| a + t \frac{a}{ \| a \| } \| - \| a \| }{ t } = \lim_{ t \to 0 } \frac{ ( \| a \| - t ) - \| a \| }{ t } $$ ... ... ... indeed, specifically how $$\| a + t \frac{a}{ \| a \| } \| = ( \| a \| - t )$$ ... ...
Help will be appreciated ...
Peter
Attachments
Last edited: