?y, dy, ?

[rubing]

I am working on some problems from Keisler's free Elementary Calculus on pg 59.

The following problem they ask you to: 'express ?y and dy as functions of x and ?x, and for ?x infinitesmial find and infinitesimal ? such that ?y = dy + ??x'

problem 1: y = x²

My answer was:

?y = 2x?x + ??x, dy = 2x?x, ???

Compared to the answer in the manual:

?y = 2x?x + ?x², dy = 2x?x, ?y = dy + ?x<sup>2


, so it looks like i got dy correct which is the change in the tangent line, but i don't quite grasp the other 2 parts to this question.</sup>

 

[rubing]

Is this question unclear? Do I need to provide more background?? thanks!

 

[pka]

I am working on some problems from Keisler's free Elementary Calculus on pg 59.

I have a hardback instructor's copy of that textbook.
According to it the expected answer is:
\(\displaystyle \Delta y=2x\Delta x+(\Delta x)^2,~dy=2x\Delta x,~\&~\Delta y=dy+(\Delta x)^2\)

Keisler lays out to process on page 58, examples 3&4.
What is your question now?