## Calculus (3rd Edition)

Solve the equations given by the two conditions The first condition: $|a − 5| < \frac{1}{2}$ $a-5-\frac{1}{2}$ $a<5\frac{1}{2}$ and $a>4\frac{1}{2}$ The second condition: $|b − 8| < \frac{1}{2}$ $b-8-\frac{1}{2}$ $b<8\frac{1}{2}$ and $b>7\frac{1}{2}$ The hint is to use the triangle inequality $(|a + b|≤|a| +|b|)$, but I did not use the hint. To prove $|(a + b) − 13| < 1$, we take the greatest values that a and b could possibly be. $|<5\frac{1}{2}+<8\frac{1}{2}-13|$ $|<14-13|$ To prove $|(a+b)−13|<1$, we also take the least values that a and b could possibly be. $|>4\frac{1}{2}+>7\frac{1}{2}-13|$ $|>12-13|$ These value has to be $<1$.