MAT 21A Lecture 3: MAT21A - Lecture 3 - 2.3: The Precise Definition of a Limit
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Mat21a - lecture 3 - 2. 3: the precise definition of a limit. (cid:1006) = (cid:1006)(cid:1009) means: in order to force (cid:1006) to be as close as we want to 25 (without necessarily actually equalling 25), we just need to make x close enough to 5 (without equalling (cid:1864)(cid:1865) (cid:1009) The goal is to force (cid:1006) to be within 2 of 25. Force (cid:1006) to be within 23 and 27 ( 23 < (cid:1006) < 27) Start with original inequality: 23 < (cid:1006) < 27. Next, square root inequality to get rid of (cid:1006) : (cid:1006)(cid:1007)< (cid:1006) < (cid:1006)(cid:1011) Then, you new inequality should look like this: (cid:1006)(cid:1007) < x < (cid:1006)(cid:1011) However, to take into account the , our inequality could be both of the following: Since we want x close to 5, we will use this inequality: (cid:1006)(cid:1007) < x < (cid:1006)(cid:1011) x is close to 5 x is close to -5.
