Answer by Anonymous for Spivak's calculus Chapter 1 exercise 21 proof...
Your proof is essentially correct, except for some minuscule, easily corrected mistakes.When you write $|x - x_0||y - y_0| < |y - y_0|$, you're assuming $y - y_0 \ne 0$.Your last inequality before...
View ArticleSpivak's calculus Chapter 1 exercise 21 proof verification
Prove that if$$|x - x_0| < \min \left(\frac{\varepsilon}{2(|y_0| + 1)}, 1\right)$$ and $$ |y - y_0| < \frac{\varepsilon}{2(|x_0| + 1)}$$then $|xy - x_0 y_0| < \varepsilon$My proof: $xy -...
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