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Unformatted text preview: Then, x k as x . lim x c x k has Limit Form c , which implies that the limit is 0 (regardless of whether c is positive, negative, or 0). Also, x k as x , if x k is defined as a real quantity whenever x < 0 . Then, lim x c x k has Limit Form c , which implies that the limit is 0. If x k is undefined as a real quantity whenever x < 0 , then lim x x k does not exist (DNE), and lim x c x k does not exist (DNE), even if c = 0 . 5. Irrational Exponents; Roots of Negative Real Numbers. It is true that x k and lim x c x k = 0 (for any real constant c ) for any positive real constant k . But what if k is irrational? For example, if k = , then how do we define something like 2 when x = 2? Remember that = 3.14159. ... Consider the corresponding sequence: 2 3 = 8 2 3.1 = 2 31 10 = 2 31 10 8.57419 2 3.14 = 2 314 100 = 2 157 50 = 2 157 50 8.81524...
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- Fall '10