with detailed solution handwritten neat and clean

Ill. Given that lim f(x) = 7, lim g(x) = -6, X- -00 x- -0 find the limits that exists. If the limit does not exist, explain why. 1. lim [2f (x) - g(x)] X - -00 2. lim [x2 + g(x)] X - -00 3. lim [69(x) - 7g(x)] X- -00 4. lim g(x) x- -co f (x) 5. lim If (x) - 9(x) X- -00 x 6. lim xf(x) X--00 (2x+3)g(x)I. Complete the table by computing f (x) at the given values of x. Use the results to guess the indicated limits, if they exist. 1 1. f ( x) = - x2+ 1 x-+00 lim f(x) and lim f(x) X - -00 X 1 10 100 1000 f (x) X -1 -10 -100 -1000 f (x) 2. f(x) = 3x3 - x2 + 10; lim f(x) and lim f(x) X 1 10 100 1000 f (x) X -1 -10 -100 -1000 f (x) x-+00 ll. Given that lim f(x) = 3, lim g(x) = -5, and lim h(x) = 0, find the limits that exists. If the limit does not exist, explain why. x -+ + 00 1. lim f(x) + 3g(x) x -+00 2. lim f(x) . h(x) x -+00 3. lim [g(x) ]2 x -+00 3 4. lim x-+oog (x) 6h(x) 5. lim x-+0 5f (x) +3g(x)