anonymous
  • anonymous
lim f(x) as x-> 2- and lim f(x) as x-> 2+ help explain graphs of limits to me?
Mathematics
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anonymous
  • anonymous
lim f(x) as x-> 2- and lim f(x) as x-> 2+ help explain graphs of limits to me?
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
anonymous
  • anonymous
So how does the graph explain what the limit is?
ganeshie8
  • ganeshie8
For \(\large \lim\limits_{x\to 2^{-}} f(x)\), imagine yourself walking on the graph towards x=2 from the left of "x=2" |dw:1433302549455:dw|

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anonymous
  • anonymous
Okay, that is helpful. Can you explain what the dot on the graph represents?
ganeshie8
  • ganeshie8
you're staying on y=f(x)=3, so the left limit is 3 : \[\large \lim \limits_{x\to2^{-}}f(x) ~~=~~3\]
ganeshie8
  • ganeshie8
similarly see if you can find the right limit : \[\large \lim \limits_{x\to2^{+}}f(x) ~~=~~?\]
anonymous
  • anonymous
-3 ?
ganeshie8
  • ganeshie8
Excellent! the "dot" represents the value of function exactly at x = 2
ganeshie8
  • ganeshie8
|dw:1433302827174:dw|
anonymous
  • anonymous
Oh okay. so for this one would it be 4?
ganeshie8
  • ganeshie8
Yes! the right hand side limit is 4
anonymous
  • anonymous
Okay, now i understand what the difference in the two limits is. Thank you!
ganeshie8
  • ganeshie8
Yw!

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