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hawkfalconBest ResponseYou've already chosen the best response.0
\[\lim_{x \rightarrow 5} \frac{ x5 }{ \left x5 \right }\]
 one year ago

vf321Best 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?
 one year ago

vf321Best ResponseYou've already chosen the best response.1
Okay. Then coming in from the right at 5, what is your limit equal?\[\lim_{x \rightarrow 5^+} \frac{ x5 }{ \left x5 \right }=?\]
 one year ago

hawkfalconBest ResponseYou've already chosen the best response.0
oh wait. \[infinity\]
 one year ago

vf321Best 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.
 one year ago

vf321Best 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?
 one year ago

hawkfalconBest ResponseYou've already chosen the best response.0
okay. Wait each side would be infinity right?
 one year ago

vf321Best 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.
 one year ago

hawkfalconBest ResponseYou've already chosen the best response.0
at 6 it would be 1/2
 one year ago

hawkfalconBest ResponseYou've already chosen the best response.0
I read that it has to be either DNE, infinity, or negative infinity
 one year ago

hawkfalconBest ResponseYou've already chosen the best response.0
@vf321 sorry, i'm confused :(:#
 one year ago

vf321Best ResponseYou've already chosen the best response.1
Lets try this again.\[\frac{65}{65}=1\] how on earth did u get 1/2?
 one year ago

hawkfalconBest ResponseYou've already chosen the best response.0
I was accidentally looking at a different problem:3
 one year ago

hawkfalconBest ResponseYou've already chosen the best response.0
But okay, then 5.0001 = 1 too.
 one year ago

vf321Best ResponseYou've already chosen the best response.1
okay. try 5.000000000000000001
 one year ago

hawkfalconBest ResponseYou've already chosen the best response.0
Anything >5 will be 1
 one year ago

vf321Best ResponseYou've already chosen the best response.1
good. In fact, you can say\[\lim_{x \rightarrow 5^+} \frac{ x5 }{ \left x5 \right }=1\]
 one year ago

vf321Best ResponseYou've already chosen the best response.1
Now try\[\lim_{x\rightarrow 5^}f(x)=?\]From the left, on your own.
 one year ago

hawkfalconBest ResponseYou've already chosen the best response.0
o.o okay that makes sense. Let me try...
 one year ago

hawkfalconBest ResponseYou've already chosen the best response.0
So it's DNE, because they are different.
 one year ago

vf321Best 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.
 one year ago

vf321Best ResponseYou've already chosen the best response.1
no but its for ur understanding.
 one year ago

hawkfalconBest ResponseYou've already chosen the best response.0
Oh okay, thank you:)
 one year ago

vf321Best ResponseYou've already chosen the best response.1
remeber to close the question.
 one year ago
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