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[SOLVED] 1.6.365 AP Calculus Exam Limits

karush

Well-known member
Jan 31, 2012
2,678
ok I chose c being false, since a limit does not exist if f(x) is different coming from $\pm$
 
Last edited:

Greg

Perseverance
Staff member
Feb 5, 2013
1,382
You need to look at left-hand and right-hand limits. I don't see where "$\pm$" comes into it.
 

HallsofIvy

Well-known member
MHB Math Helper
Jan 29, 2012
1,151
I believe that "from the left and from the right" was what Karush meant by "[tex]\pm[/tex]!

Yes, Karush, "c" is the only one that is false.

a) [tex]\lim_{x\to 2} f(x)[/tex] exists.
True. The limit is 2. (f(2)= 1 so f is NOT continuous there.)

b) [tex]\lim_{x\to 3} f(x)[/tex] exists.
True. The limit is 5. (Further f(3)= 5 so f is continuous there.)

c) [tex]\lim_{x\to 4} f(x)[/tex] exists.
False. The "limit from the left", [tex]\lim_{x\to 4^-} f(x)[/tex], is 2 while the "limit from the right", [tex]\lim_{x\to 4^+} f(x)[/tex], is 4. Since the two one-sided limits are not the same the limit itself does not exist.

d) [tex]\lim_{x\to 5} f(x)[/tex] exists.
True. The limit is 6. (Further f(5)= 6 so f is continuous there.)

e) f is continuous at x= 3.
True. As I said in (b), [tex]\lim_{x\to 3} f(x)[/tex] and f(3) both exist and are equal.
 

karush

Well-known member
Jan 31, 2012
2,678
ok I think the big visual hint on this one was the obvious disconnected gap.

mahalo everyone the comments really increase the insight on these.