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2.3 Exercises 1. Given that (e) lim [x2f (x) ] (f) f(- 1) + lim g(x) - 2 lim f(x) = 4 lim g(x) = -2 lim h(x) = 0 - 2 *-+ 2 find the limits that exist. If the limit does not exist, explain y = f(x) y = g(x) why. * - 2 (a) lim [f (x) + 5g(x)] (b) lim [g(x)]3 (c) lim of(x) (d) lim 3f (x) 2- 2 x-2 g(x) 3-9 Evaluate the limit and justify each step by indicating the g(x) g (x) h(x) appropriate Limit Law(s). (e) lim 1-2 h(x ) - 2 f ( x ) 3. lim (4x2 - 5x) 4. lim (2x3 + 6x2 - 9) 2. The graphs of f and g are given. Use them to evaluate each 5. lim (v2 + 20) (203 - 5) 3+2 + 1 0 - 2 6. lim limit, if it exists. If the limit does not exist, explain why. 1-7 + 2 - 5+ + 2 (a) lim [f(x) + g(x)] (b) lim [f (x) - g(x)] 7. lim V9 - u3 + 2u2 4 - - 2 8. lim Vx + 5 (2x2 - 3x) x -+ 3 21 5 - 1 4 ) 3 9. lim (c) lim [f(x)g(x)] (d) lim f( x) 1 - - 1 5+2 + 4 1 -+ 3 g(x)