anonymous
  • anonymous
Find the indicated limit, if it exists. lim x->2 {x+3 x< 2 } {3-x x>_ 2}
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
Plug in \(x=2\) to both cases and see what happens.
anonymous
  • anonymous
@wio you get 5 and 1.
anonymous
  • anonymous
Do you know where I got \(2\) from?

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anonymous
  • anonymous
the limit as x approaches 2?
anonymous
  • anonymous
Yes
anonymous
  • anonymous
But there is another reason as well, both cases are split on 2.
anonymous
  • anonymous
So we need to see if both cases approach 2 on both sides.
anonymous
  • anonymous
The limit only exists if both sides approach the same number. You can graph it to see as well.
anonymous
  • anonymous
how would you graph it?
anonymous
  • anonymous
|dw:1434583292694:dw|
anonymous
  • anonymous
so it DNE?
anonymous
  • anonymous
@wio
anonymous
  • anonymous
Yes
anonymous
  • anonymous
Does it make sense how I graph it?
anonymous
  • anonymous
Yea, can you help me with another one?
anonymous
  • anonymous
lim x-> 0 {5x-9 x<0} { l 2-x l x>_0}
anonymous
  • anonymous
|dw:1434583971277:dw|
anonymous
  • anonymous
is that right? @wio
anonymous
  • anonymous
Yes, that looks right
anonymous
  • anonymous
do it DNE too?
anonymous
  • anonymous
Yeah
anonymous
  • anonymous
You don't have to graph it though, you can just plug in 0 and if both cases have a different value, then the limit doesn't exist.
anonymous
  • anonymous
|dw:1434584238267:dw|
anonymous
  • anonymous
lim x->5 { 5-x, x<5} { 8 , x=5} {x+3, x>5}
anonymous
  • anonymous
is that right? @wio
anonymous
  • anonymous
so it DNE right?
anonymous
  • anonymous
It is DNE, though the graph isn't quite right
anonymous
  • anonymous
8 and x+3 meet at x=5
anonymous
  • anonymous
oh ok thank you so much!

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