Solve the following inequality and equation:

Question 1. 5+7=12 marks
Solve the following inequality and equation:
a) −4 ≤ 3−
1 2x
< 0 b) ||x−1|−|x + 1|| = x2
Question 2. 2+3+3+4=12 marks
Calculate the following limits or show that they do not exist. Do not use l’Hoˆpital’s rule.
a) lim x→3|1−x| b) lim x→1
x−13 √x−1 c) lim x→0
sin2x xcosx
d) lim x→π/2 1 cosx −tanx


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