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3.4 EXERCISES 1. Explain in your own words the meaning of each of the following. (a) lim f(x) = 5 b) lim f(x) = 3 2. (a) Can the graph of y = f(x) intersect a vertical asymptote? Let's Can it intersect a horizontal asymptote? Illustrate by sketching graphs. NA (b) How many horizontal asymptotes can the graph of y = f(x) have? Sketch graphs to illustrate the possibilities. 3. For the function f whose graph is given, state the following. (a) lim f(x) (b) lim f(x) A 5. Guess the value of the limit * - - 0 (c) lim f(x) (d) lim f(x) x - 3 lim x - >co 2 * (e) The equations of the asymptotes by evaluating the function f(x) = x2/2* for x = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 50, and 100. Then use a graph of f to support your guess. 6. (a) Use a graph of f (x ) = ( 1 - 2) 1 to estimate the value of limx-.f (x) correct to two decimal places. (b) Use a table of values of f (x) to estimate the limit to four decimal places. 7-8 Evaluate the limit and justify each step by indicating the 4. For the function g whose graph is given, state the following. appropriate properties of limits. (a) lim g(x) (b) lim g(x) * - - 00 2x2 - 7 9x' + 8x - 4 (c) lim g(x) (d) lim g(x) 7. lim 8. lim x - 2 - x ->oo 5x2 + x- 3 x - 00 3- 5x + x3 (e) lim g(x) (f) The equations of the asymptotes r- 2+