Help with Limit Test | Solving Limits

[Llama77]

I am having trouble with this limit, i am to do a Limit test but I just don't see it.


Step 1.
Lim sqrt(x) / x
x --> Infinity




Step 2.
My professor this goes down to

Lim 1 / sqrt(x)
x --> Infinity


and the limit is then 0





What I am not sure about is from steps 1 to step 2.




I tried the latex it wouldn't work for me, sorry.

 

[Moo Of Doom]

Your professor simply divided the numerator and the denominator both by $\sqrt{x}$.

 

[tacman]

No problem, I'm happy to help with understanding the limit test. The key idea behind the limit test is to simplify the original expression and then take the limit as x approaches infinity. In this case, you started with the expression sqrt(x)/x and simplified it to 1/sqrt(x). This is a valid step because we can rewrite sqrt(x) as x^(1/2) and then use the power rule for limits to simplify the expression.

So, from step 1 to step 2, you essentially just simplified the original expression using algebra and basic limit rules. The limit of 1/sqrt(x) as x approaches infinity is 0 because the denominator (sqrt(x)) grows much faster than the numerator (1). Therefore, the overall fraction approaches 0 as x gets larger and larger.

I hope this helps clarify the steps for the limit test. Just remember to simplify the original expression and then take the limit as x approaches infinity. Let me know if you have any other questions or need further assistance. Good luck with your studies!