SOLUTION 1 Preliminary analysis of the problem guessing a value for 6 Let be a given positive number We want to find a number such that if 0 x 4 8 then 3x 10 2 E But 3x10 2 3x 12 3 if 0 x 41 6 then 3 that is if 0 x 41 6 then This suggests that we should choose 3 2 Proof showing that works Given 0 choose If 0 If 3 3x10 2 3 3 E E Therefore we want such that 36 Thus if 0 x 4 6 then 3x 10 21 E Therefore by the definition of a limit we get the following lim 3x 10 2 x 4 E 23 6 then we get the following