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hawkfalcon
 2 years ago
Best ResponseYou've already chosen the best response.0\[\lim_{x \rightarrow 5} \frac{ x5 }{ \left x5 \right }\]

vf321
 2 years ago
Best ResponseYou've already chosen the best response.1Well, do you know that\[\lim_{x\rightarrow a}f(x)=\lim_{x\rightarrow a^+}f(x)\cap\lim_{x\rightarrow a^}f(x)\]I.e., for 1 variable, the bilateral limit exists iff both lateral limits exist and are the same?

vf321
 2 years ago
Best ResponseYou've already chosen the best response.1Okay. Then coming in from the right at 5, what is your limit equal?\[\lim_{x \rightarrow 5^+} \frac{ x5 }{ \left x5 \right }=?\]

hawkfalcon
 2 years ago
Best ResponseYou've already chosen the best response.0oh wait. \[infinity\]

vf321
 2 years ago
Best ResponseYou've already chosen the best response.1The rightside limit is not DNE. When solving limits you can only say that\[\lim_{x\rightarrow a}f(x)=f(a)\] if f(a) exists.

vf321
 2 years ago
Best ResponseYou've already chosen the best response.1Think about it. We're approaching the limit from the right. When x = 6, what's the limit? When x = 5.01, what's the limit?

hawkfalcon
 2 years ago
Best ResponseYou've already chosen the best response.0okay. Wait each side would be infinity right?

vf321
 2 years ago
Best ResponseYou've already chosen the best response.1Try plugging in values I showed you. Also, a note for the prior statement I made: f has to be continuous.

hawkfalcon
 2 years ago
Best ResponseYou've already chosen the best response.0at 6 it would be 1/2

hawkfalcon
 2 years ago
Best ResponseYou've already chosen the best response.0I read that it has to be either DNE, infinity, or negative infinity

hawkfalcon
 2 years ago
Best ResponseYou've already chosen the best response.0@vf321 sorry, i'm confused :(:#

vf321
 2 years ago
Best ResponseYou've already chosen the best response.1Lets try this again.\[\frac{65}{65}=1\] how on earth did u get 1/2?

hawkfalcon
 2 years ago
Best ResponseYou've already chosen the best response.0I was accidentally looking at a different problem:3

hawkfalcon
 2 years ago
Best ResponseYou've already chosen the best response.0But okay, then 5.0001 = 1 too.

vf321
 2 years ago
Best ResponseYou've already chosen the best response.1okay. try 5.000000000000000001

hawkfalcon
 2 years ago
Best ResponseYou've already chosen the best response.0Anything >5 will be 1

vf321
 2 years ago
Best ResponseYou've already chosen the best response.1good. In fact, you can say\[\lim_{x \rightarrow 5^+} \frac{ x5 }{ \left x5 \right }=1\]

vf321
 2 years ago
Best ResponseYou've already chosen the best response.1Now try\[\lim_{x\rightarrow 5^}f(x)=?\]From the left, on your own.

hawkfalcon
 2 years ago
Best ResponseYou've already chosen the best response.0o.o okay that makes sense. Let me try...

hawkfalcon
 2 years ago
Best ResponseYou've already chosen the best response.0So it's DNE, because they are different.

vf321
 2 years ago
Best ResponseYou've already chosen the best response.1yes! and, if you were to graph the function on a CAS (or WolframAlpha), you'd see there's a jump discontinuity at 0.

vf321
 2 years ago
Best ResponseYou've already chosen the best response.1no but its for ur understanding.

hawkfalcon
 2 years ago
Best ResponseYou've already chosen the best response.0Oh okay, thank you:)

vf321
 2 years ago
Best ResponseYou've already chosen the best response.1remeber to close the question.
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