Dror Bar-Natan: Classes: 2002-03: Math 157 - Analysis I:

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Partial Solution of Homework Assignment 1

this document in PDF: Sol01.pdf

Warning: The solutions presented here are partial at best. They are only intended for use as checks and hints and are often incomplete.

Question 1-11-ii: $\{x: -5<x<11\}$.

Question 1-11-iv: $\{x: x<1$ or $x>2\}$.

Question 1-11-vi: The empty set.

Question 1-11-viii: Same solutions as for $(x-1)(x+2)=3$, which is a simple quadratic equation.

Question 1-12-iv: Replace $y$ by $-y$ in $\vert x+y\vert\leq\vert x\vert+\vert y\vert$.

Question 1: Write $ax^2+bx+c=a\left(x+\frac{b}{2a}\right)^2-\frac{b^2-4ac}{4a}$ and use the fact that $\left(x+\frac{b}{2a}\right)^2$ is always positive (except for one value of $x$).

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