Please correct my mistake with this limit

Step-by-step explanation:

The first four lines are correct.  Your mistake is after you get to this part:

lim(n→0) (2 sin²(n/2) / n)

In the fifth line, it looks like you try to write this limit as:

2 lim(n→0) ¼ (sin (n/2) / (n/2))²

But these are not the same.  You're introducing another n in the denominator.

Here's what you should do instead:

lim(n→0) (2 sin²(n/2) / n)

lim(n→0) (sin²(n/2) / (n/2))

lim(n→0) (sin (n/2) / (n/2)) × lim(n→0) (sin (n/2))

1 × 0

0

Now when you plug this in, you get (0 + 1) / (0 − 1) = -1.

Look it up on internet

Step-by-step explanation: INTERNET