Find the limit

[alexmay]

Hello, I am trying to figure out how to work my way through this problem and would appreciate assistance.

lim √x+64 -8
x->0 x


It is the square root of x +64 and then -8 is not included under the radical, all over x.

 

[MarkFL]

Let's write the limit:

[MATH]L=\lim_{x\to0}\frac{\sqrt{x+64}-8}{x}[/MATH]
Try rationalizing the numerator...

 

[pka]

WRT reply #2, if your algebra is weak, L'Hopital's rule gives the same answer.

 

[alexmay]

Okay, I know how to rationalize. I went ahead and rationalized and worked out the problem and my final answer is 1/16, I'm not sure if it is correct or not.

 

[pka]

Okay, I know how to rationalize. I went ahead and rationalized and worked out the problem and my final answer is 1/16, I'm not sure if it is correct or not.

That is the correct answer.

 

[Steven G]

Okay, I know how to rationalize. I went ahead and rationalized and worked out the problem and my final answer is 1/16, I'm not sure if it is correct or not.

You can always check your answer. Plug x=.0001 (any number close to 0 will work) into the original and then subtract 1/16. If you get close to 0 you have the right answer. If you feel that the subtraction is not close enough to 0, then choose a smaller x, like .0000001.