2) Sketch the graph of a function f that satisfies all of the following conditions: lim f (x) = -00, lim f (x) = 00, lim f (x) = -0, lim f (x) = 0 x- 2" I+-2 lim f (x) = 0. lim f (x) = 0. f (0) = -- 3) Evaluate the given limits algebraically. a) lim 5x - 1 b) lim x* - 4x + 4 141 x'+x-6 2x c) lim x x - 3x+1 6x2 d) lim x- 3x -3x + 1 6x e) lim x4 -x 3x- -3x +1 f) lim Vx - 9 x4 - 3 2x-6X x + 4 - 2 g) lim X h) lim 4 -X x-4- 14 - x i) lim (Vx' + 4x + 1 - x) 4) For the limit lim -1 x+0 - = 2, find the value of 6 that corresponds to &=0.1. Draw a picture of the graph about the limiting value X=0 with appropriate horizontal lines representing an interval for &=0.1 about the limit of y=2 and use your calculator to determine the corresponding interval for 6. 5) Find a number o such that if 0-1' a =-1 cos x if x0 11) Use continuity to evaluate the limit. a) lim In 4 - 2x2 1 + x b ) lim cos(x - sin (2x)) 12) For what value of the constant c is the function f continuous on (-00, co) ? cc' + 2x f (x) = if x