True-False Quiz; Ch 2.3 (the definition of limit)

These are just for practice and don't affect your grade. I'm assuming you've read over Edwards and Penney, Ch  2.3, and attended my first 3-4 Calculus One lectures.  Recall that "$" means "There Exists" and """ means "For All".  After the quiz, see the bottom of the page.

True False. " e > 0, e > 1.

True False. $ e > 0, e > 1

True False.  " e > 0, $ d > 0, d < e.

True False.  $ d > 0, " e > 0, d < e.

True False. If | x-2 | < 2 then | x+5 | < 10 

True False. If | x-2 | < 1 then | 2x-4 | < 2 

True False. $ d > 0,  if | x-2 | < d, then | 2x-4 | <  2. 

True False. $ d > 0,  if | x-2 | < d, then | 2x-4 | <  4.

True False. " e > 0, $ d > 0,  if | x-2 | < d, then | 2x-4 | <  e.

True False. 2x ® 4, as x ® 2 [which means, lim 2x = 4 (with "x ® 2" underneath "lim")]

Now, give a reason for each of your correct answers. As a hint, here are the reasons I would give (but not listed in the correct order !)

T - set d = 2
T - given e, set d = e/2.
T - this means the same as the previous line.
T - given e, let d = e/2
 F - given d, setting e = d/2 makes a contradiction
T - (compare solution sets) if  0<x<4 then -15<x<5
F - let e = 0.5
T - let e = 5
T  - multiply the first inequality by 2
T - compare with the previous line (set d = 1)

Written by S Hudson. Some parts may have been translated from TEX by TTH, version 3.05.  Last modified on

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