Hello. These are practice questions from the internet. Can you please help me with them? The answers are already provided. I just need an explanation. Please provide an explanation for the answers so that I can understand, and please don't use cursive as I can't read that.

1. Evaluate the following limits if they exist. 312 - 6.r + 8 (a) lim (Do not use L'Hospitals Rule) Answer: 3 T-00 T- - 41 + 7 2 - 8.r + 12 (b) lim x 12 x2 - 3r + 2 (Do not use L'Hospitals Rule) Answer: -4 (c) lim Inc tan(wr/2). Answer: 4 IN (d) lim r cos Answer: 0 (e) lim ". Answer: 1 r-1 (f) lim VI - 1 (Do not use L'Hospitals Rule) Answer: 2 c-+1 tane - T (g) lim -. Answer: (h) lim (cosr) /. Answer: 1/ ve (i) Visin Answer: 0 5.x 5r + Inc (j) lim Answer: -5 1-x3. Show that the function is continuous on R. f(x) x sin(1/x), if x / 0 if x = 010. Use linear approximation to estimate (a)