Answer by Chris Swanson for Help with Spivak's Calculus: Chapter 1 problem 21
I just solved this today - which for me was really amazing because I was just as lost as the earlier post - so please forgive my enthusiasm. The breakthrough for me was the hint $|x - x_0|$ < 1 and...
View ArticleAnswer by Shane T for Help with Spivak's Calculus: Chapter 1 problem 21
I think I figured it out thanks to GeoffRobinson's hint, and from RJS (thanks guys!) so I figured I'd write out my own work here.$|xy-x_0y_0| = |x(y-y_0) + y_0(x-x_0)| \leq |x(y-y_0)| + |y_0(x-x_0)|$So...
View ArticleAnswer by Rhys Steele for Help with Spivak's Calculus: Chapter 1 problem 21
By reverse triangle inequality $|x| - |x_0| \leq |x-x_0| < 1$ giving $|x| < 1 + |x_0|$. Now \begin{align*}|xy - x_0y_0| & = |x(y-y_0) + y_0(x-x_0)| \leq |x||y-y_0| + |y_0||x-x_0| \\ &...
View ArticleHelp with Spivak's Calculus: Chapter 1 problem 21
I've been stuck on this problem for over a day, and the answerbook simply says "see chapter 5" for problems 20,21, and 22. But I want to complete the problem without using knowledge given later in the...
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