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

vf321 Group TitleBest ResponseYou've already chosen the best response.1
Well, 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?
 2 years ago

hawkfalcon Group TitleBest ResponseYou've already chosen the best response.0
Erm, yes.
 2 years ago

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

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

hawkfalcon Group TitleBest ResponseYou've already chosen the best response.0
would it be DNE?
 2 years ago

vf321 Group TitleBest ResponseYou've already chosen the best response.1
The 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.
 2 years ago

vf321 Group TitleBest ResponseYou've already chosen the best response.1
Think 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?
 2 years ago

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

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

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

hawkfalcon Group TitleBest ResponseYou've already chosen the best response.0
right?:3
 2 years ago

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

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

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

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

vf321 Group TitleBest ResponseYou've already chosen the best response.1
okay. now try 5.0001
 2 years ago

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

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

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

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

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

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

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

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

hawkfalcon Group TitleBest ResponseYou've already chosen the best response.0
Do I write that?:O
 2 years ago

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

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

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