# Thread: [SOLVED] The Squeeze Theorem

1. ## [SOLVED] The Squeeze Theorem

I have an explanation of how to solve this but don't understand one of the steps in it:

$\lim {x\to1} |x-1| \sin^2 x+1$

I don't understand how it follows that $1\leq|x-1|\sin^2 x+1 \leq |x-1|+1$

2. Originally Posted by Mike9182
I have an explanation of how to solve this but don't understand one of the steps in it:

$\lim {x\to1} |x-1| \sin^2 x+1$

I don't understand how it follows that $1\leq|x-1|\sin^2 x+1 \leq |x-1|+1$
Since

$
0 \le \sin^2 x \le 1
$

then (multiply by $|x-1|$ )

$
0 \le |x-1|\sin^2 x \le |x-1|
$

$