Properties of Limits Let lim((z) = L, lim,(2) = M, and c and d be two constants, and n a positive integer. 1. lim, tac = c 2. limz +a (f(z) + g(z)) =lim, af(x) +limz ,ag(x) = L + M 3. lim, a c. f(x) = c-lim, +a f(x) = c . L a. lim, a (c . f(x) + d . g(z)) = c . L= c . L +d . M 4. limz a (f(x) . g(z)) =limz "af(x)-lim, tag(z) = L . M 5. lim, a [f(x)]" = Ln f(z) lim, +. f(z) 6. limz +0. (z) lim, ". 9(z) My provided that M # 0 7. limz a (f(z) + g(z)) =limz +af(z) +limz +.9(x) = L + M Question: Use the properties above to calculate the following limits. Submit your detailed scratchwork below. 2 -42+3 1. limz-+2 4x-2 2. lim, 2(2x2 - z) 3. limz 2 ( 2 ) (212 -2)) 4. limz ,2 ((2x2 - 2)3)