Evaluate the limit((Sqrt(4+x))-2)/(x)



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thilina-g's profile pic

Posted on (Answer #1)

You have not included the limit. But by looking at the question I can see that the intended limit is 0.


If you try to evaluate the limit straight away, you will see that it will result in 0/0 situation which is indertminate. To remove this, we can multiply both numerator and denominator by `(sqrt(4+x)+2)` .


This would give,



This simplifies into,


Now you can evaluate the limit easily,

`lim_(x-gt0)1/(sqrt(4+x)+2) = 1/(2+2) = 1/4`



`lim_(x-gt0)(sqrt(4+x)-2)/x = 1/4`


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