# 1) Explain in your own words what is meant by the equation lim,-2 f (x) = 5. Is it possible for this statement to be true and yet f(2) = 3? Explain. # 2) Explain what is meant to say that lim,-1- f(x) = 3 and lim,-1- f(x) = 7. In this situation is it possible that lim,-. f(r) exists? Explain. # 9. 10,11,12) Sketch the graph of an example of a function S that satisfies the conditions: # 9) limz-1- f(x) = 2, lim,-.1+ f(x) = -2, and f(1) = 2. # 10) lim,4.0- f(x) = 1, limz-.0. f(x) = -1, lims-2 f(=) = 0, lim,-2+ f(x) = 1. f(2) = 1, f(0) is undefined. # 11) lims-3+ f(x) = 4, lim,-3- f(x) = 2, lims--2 f(x) = 2, f(3) = 3, f(-2) = 1. # 12) lims-+ f(x) = 3, lim,-4 f(z) = 3, limz-4. f(x) = -3. f(1) = 1, f(4) = =1. # 14) Guess the value of the limit lim,-2 (if it exists) by evaluating the function at the numbers: x = 2.5, 2.1, 2.05, 2.01, 2.005, 2.001, 1.9, 1.95, 1.99, 1.995, 1.999 (correct to six decimal places) 2.3 Calculating limits using limit laws: # 1) Given that lim,-+. f(x) = -3, lim,-a g(7) = 0, lim, .. h(x) = 8 find the limits that exist. If the limit does not exist, explain why. (a) lim.-alf(r) +h(=)] (b) lim,-a f (x ) |2 (c) limz -". V/h(I) (d) lim, ". (I) f (I) 9 (I) f(I) 2f (1 ) (e) lim,-h(I) (f) lime- f ( I) (g) lim " g(I) (h) lime-"h(I) -f(I) # 2) The graph of / and g are given. Use them to evaluate each limit (in the back), if it exists. If the limit does not exist, explain why. y = P(x) y = g ( x ) on (a) lim,-lf (r) + g(r)] (b) lim,-/f(x) + g(z)| (c) lim,zolf (r)g(x)] (e) lim,mar'S(x)] (f) limLV/3+ 1 (x) (d) lima(I)