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what does lim x goes to 0+ mean?

 Jan 13, 2015

Best Answer 

 #2
avatar+23254 
+5

It means to find the lim of the function as you approach 0 from the right side of the number line.

That is, as x gets closer to zero, as you approach from 0.1, then 0.01, then 0.001, then 0.0001, etc.

limx→0+x = 0  because x becomes 0.1, 0.010.001, 0.0001, ... → 0

An example:  limx→0+(1/x)  =  

  when x = 0.1 ---> lim becomes 1/0.1 = 10

  when x = 0.01 ---> lim becomes 1/0.01 = 100

  when x = 0.001 ---> lim becomes 1/0.001 = 1000

  so the lim approaches ∞.

However, limx→0-(1/x)  =  

  when x = -0.1 ---> lim becomes 1/-0.1 = -10

  when x = -0.01 ---> lim becomes 1/-0.01 = -100

  when x = -0.001 ---> lim becomes 1/-0.001 = -1000

  so the lim approaches -∞.

Thus the  limx→0(1/x)  doesn't exist, because you get a different value when you approach from the right side than you do when you approach from the left side.

 Jan 14, 2015
 #1
avatar+130477 
+5

In simplest terms, it means..."What value does a function approach as it "nears" 0 from the right side??"

This might be a number, or it could be something else... (infinity, for example)

 

 Jan 14, 2015
 #2
avatar+23254 
+5
Best Answer

It means to find the lim of the function as you approach 0 from the right side of the number line.

That is, as x gets closer to zero, as you approach from 0.1, then 0.01, then 0.001, then 0.0001, etc.

limx→0+x = 0  because x becomes 0.1, 0.010.001, 0.0001, ... → 0

An example:  limx→0+(1/x)  =  

  when x = 0.1 ---> lim becomes 1/0.1 = 10

  when x = 0.01 ---> lim becomes 1/0.01 = 100

  when x = 0.001 ---> lim becomes 1/0.001 = 1000

  so the lim approaches ∞.

However, limx→0-(1/x)  =  

  when x = -0.1 ---> lim becomes 1/-0.1 = -10

  when x = -0.01 ---> lim becomes 1/-0.01 = -100

  when x = -0.001 ---> lim becomes 1/-0.001 = -1000

  so the lim approaches -∞.

Thus the  limx→0(1/x)  doesn't exist, because you get a different value when you approach from the right side than you do when you approach from the left side.

geno3141 Jan 14, 2015

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