# Math Help - Simple Interval finding?

1. ## Simple Interval finding?

I've done problems exactly like these, but these two keep giving me the wrong answer, and I'm not sure why.

1) if |x - 2| < delta then |1/x - 0.5| < 0.2
2) if |x - 4| < delta then |sqrt(x) - 2| < 0.4

In both I need to find delta.

2. Originally Posted by CFem
I've done problems exactly like these, but these two keep giving me the wrong answer, and I'm not sure why.

1) if |x - 2| < delta then |1/x - 0.5| < 0.2
2) if |x - 4| < delta then |sqrt(x) - 2| < 0.4

In both I need to find delta.
For 2.

Try multiplying $|\sqrt{x} - 2|$ by its conjugate.

Notice that

$|\sqrt{x} -2| < 0.4$

$|\sqrt{x} - 2| + 4 < 0.4 + 4$

$|\sqrt{x} + 2| < 4.4$.

So

$|\sqrt{x} - 2||\sqrt{x} + 2| < 0.4\cdot 4.4$

$|(\sqrt{x} - 2)(\sqrt{x} + 2)| < 1.76$

$|x - 4| < 1.76$.

So $\delta = 1.76$.