MAT 271 Problem Set #1: Limits Instructions: Work the following exercises out by hand on separate paper. Clearly label each exercise and indicate your final answer. You must show all work for full credit. 1. For each of the following functions, first complete the table and then, based on the table, find the given limits. If a limit does not exist, write "DNE" . 1) f (x) = X-x-6 x - 3 X 2.9 2.99 2.999 3 3.001 3.01 F (x) 3.1 a) lim f (x) = X - 3 - b) lim f (x) = c) lim f (x) = X - 3' 2) g(x) = 1x-5 x- 5 X 4.9 4.99 4.999 5 5.001 5.01 5.1 g(x) a) lim g(x) = X -5 - b) lim g(x) = x-5+ c) lim g (x) = x-5 3) h(x) = - x+1 V4x+5-1 X -1.1 -1.01 -1.001 -1 0.999 0.99 -0.9 h (x ) a) lim_h(x) = x--1- b) lim h(x) = x--1 lim h(x) = x--1II. Use the graph of f(x) below to find each of the following limits. If a limit does not exist, write "DNE" (6, 5) 4 (-4,2)0 ( 6 , 2 ) L x -4 -2 4 6 8 -2 9(1, -2 ) -4 -6 4) lim f(x) X--4 5) lim f(x) 6) lim f (x) x--4+ x--4' 7) lim f (x) 8) lim f(x) x-1- X-1+ 9) lim f (x) x-1 10) lim f (x) 11) lim f(x) 12) lim f (x) X -+ 6 - * -+ 6 + X- 6 ' Find each limit analytically. If the limit does not exist, write "DNE" . 13) lim -6x+5 x2-9 14) lim Vx2 - 10 X-4 X-3 15) lim - 2x 16) lim - X-6 X-0x2 -x X-6 Vx+3-3 17) lim 18) lim Sin(5x) x-5 x-5 X+0