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Are these two limits exist? How to prove?

 

 

1.)lim x-->∞ (sqrt(x^2 + x)) - sqrt(x^2 - dx)

 where d is a positive constant

2.)limx-->9 (xsqrt(x)-3)/(x-9)

Guest Feb 12, 2016

Best Answer 

 #1
avatar+26328 
+10

The first one exists:

 

limit

.

The second one doesn't exist as the numerator tends to a finite value and the denominator tends to 0.  Division by zero is undefined.

Alan  Feb 12, 2016
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1+0 Answers

 #1
avatar+26328 
+10
Best Answer

The first one exists:

 

limit

.

The second one doesn't exist as the numerator tends to a finite value and the denominator tends to 0.  Division by zero is undefined.

Alan  Feb 12, 2016

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