(c) Recall e = 2.71828... is Euler's constant and ed is the exponential function. Since e > 2, you may assume that lim = oo. Show that lim = 00. Hint: you may use the result of part (b) and a new Squeeze Theorem in one of the lectures.2. Here you will prove that lim = oo without any use of L'Hopital's Rule. T-+co In x (a) For all positive integers n 2 1, prove that 2" 2 2n. (b) For all real numbers x 2 1, prove that 27 2 x. Hint: Define n = [x].(d) Using the formal e - 6 definition of the limit, prove that lim = 0. x+co Inc Hint: you may need to use the result of part (c) and the logarithm is an increasing function