(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

use lim as x__>0 (sin(x))/(x) to evaluate the following : lim (x^(2) cot(x) + sin(x/2) - cos(x) + 1)/(x) as x__>0

3. The attempt at a solution

1- lim as x__>0 (x^(2) cot(x))/ (x)= x cotx = x (cosx)/(sinx)= (x/sinx) cosx = 1.1=1

And I think I can use L'Hospital's Rule to evaluate the previous one, right?

2- lim as x__>0 (sin(x/2))/(x)= 1/2 (sin(x/2))/(x/2)= 1/2.

3. this is where it gets hard. I tried to use L'Hospital's Rule, but I just want to see if that makes sense or not. lim as x__>0 (-cosx +1)/(x)= 0/0. using L'H, I will get lim as x__>0 sinx= 0 . so my final answer will be 1+1/2+-0= 1.5. Is this right?

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# Homework Help: Evaluate math limit question

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