+0  
 
+5
492
1
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lim x -> 0 x-sqrt(x) / x + sqrt(X)

 Sep 15, 2015
 #1
avatar+130516 
+5

Note that this limit only exists from the right.....

 

lim x -> 0+ x-sqrt(x) / x + sqrt(X)   multiply both by  x - sqrt x  on top and bottom

 

lim x -> 0+ [x^2 - 2xsqrt(x) + x] / [x^2 -x]   factor x out of top/bottom

 

lim x -> 0+ [x - 2sqrt(x)  + 1] / [x - 1]      let the limit go to 0

 

=  -1

 

 

Here's the graph :    https://www.desmos.com/calculator/gnp5cfkzde

 

 

 

cool cool cool

 Sep 15, 2015

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