Each of the following statements is false. Explain why, and then give a counterexample using formulas or graphs. For example, the following statement is false: if lirn f (3:) = E, 113}a_ then lirn f (3:) = E. xm'l' Indeed, a function can have different limits to the left and to the right. For instancej consider the function 23: a: g 0 m = { 3: + 1 :c > 0. Then lim f (3:) = 0, 3)!) but 311% f (93) = 1, It would also be OK to draw the graph of such a function. 1. If as its) = 2, then f (a) = E. 2. If f is not continuous at a, then $15}; f (9:) does not exist. 3. If $11}; f (9:) = f and $113 9(a) = 9, then f(a) = 9(a). 4. If $113 9(33) = 0, then lirn f($) mi-a 9(93) does not exist (it is not a real number). 5. If f($) > 0 for all a: E (oo,+oo), then lim x) > 0. 5.9)0