Limit of function as X approaches inf with square root

[Augiz]

Hello everyone,
I have this function for my homework and got no idea how to do it, anyone could explain to me on how to solve it?
I know the answer is 4 and the but the method of websites that calculates limits (wolfram, symbolab) is nowhere close to what we use or are supposed to.



Thank you lots.

 

[tkhunny]

"Supposed to use". This phrase disturbs me. Read my signature.

What methods can you use?

One common method is to multiply both numerator and denominator - separately - by the reciprocal of x to the highest power shown in the original problem statement. This is a little tricky because of the square root. You may wish to think of it this way \(\displaystyle \sqrt{x^{4}} = x^{2}\)

Lets see what you get.

 

[Dr.Peterson]

Hello everyone,
I have this function for my homework and got no idea how to do it, anyone could explain to me on how to solve it?
I know the answer is 4 and the but the method of websites that calculates limits (wolfram, symbolab) is nowhere close to what we use or are supposed to.

a) \(\displaystyle \displaystyle \lim_{x\rightarrow\infty} \dfrac{\sqrt{4x^2+x^4}+3x^2}{x^2-5x}\)

Thank you lots.

You mention "what we use or are supposed to", which I take to mean "what we have been taught, and are therefore expected to do". It will be helpful if you can tell us what that method is (perhaps by showing an example you were given, if you don't want to try applying it to this exercise). Can you do that, so we don't have to guess?