Limit that tends to infinity of (√x + x) / x

[matematiconapoletano]

How do you demonstrate that the limit in the image is 1?

I am trying to simplify but I am stalled.

Thank you!

 

[Deleted member 4993]

How do you demonstrate that the limit in the image is 1?

I am trying to simplify but I am stalled.

Thank you!


View attachment 19772

\(\displaystyle \frac{x + \sqrt{x}}{x}\)

\(\displaystyle = \ \frac{x}{x} + \frac {\sqrt{x}}{x}\)

continue.......

 

[pka]

Since \(x\to\infty\) we know that \(x>0\) which allows us to write \(\dfrac{x+\sqrt{x}}{x}=\dfrac{1+\sqrt{\frac{1}{x}}}{1}\).

 

[Steven G]

You are in calculus and are having trouble simplifying [math]\dfrac{x + \sqrt{x}}{x}[/math]. It can't be that you don't know what x/x equals so it must be that you do not know what [math]\dfrac{\sqrt{x}}{x}[/math]. This is not good at all.

 

[matematiconapoletano]

Sorry guys, you are all right, I didn't put enough thought before posting!