find the limit approaching positive infinity of f(x)-4x^2+2x-5/x

find the limit approaching positive infinity of f(x)=5x^(3/2)/4x^(1/2)+1

Question

find the limit approaching positive infinity of f(x)-4x^2+2x-5/x

find the limit approaching positive infinity of f(x)=5x^(3/2)/4x^(1/2)+1

anteater · Answer

If you do the division, you get 4x + 2 + 5/x and then think about what happens as x gets very large. The 5/x part will approach 0. The 2 remains the same. 4x will become very large, so as x --> inf, (4x^2 + 2x - 5)/x also --> inf

anteater · Answer

Now on the second one, does f(x) look like this?

$$(5x^(3/2))/(4x^(1/2) + 1)$$

anonymous · Answer

it's 5x^3/2 / 4x^1/2+1

anteater · Answer

Is the 1 in the denominator of the fraction?

anonymous · Answer

yes

anteater · Answer

Ok, thanks! Just a minute, please.

anteater · Answer

I believe for this one f(x) would also approach positive infinity as x tends to infinity. Here is why:

As x becomes very large, the + 1 in the denominator becomes negligible. So your function is looking more like 5x^3/2 / 4x^1/2 .  x^3/2 divided by x^1/2 is just x, so your function would start to look more like 5x/4 as x becomes very large. As x--> inf, 5x/4 will also --> inf.

anteater · Answer

Does that make sense?

anonymous · Answer

yes thanks

anteater · Answer

You're welcome :)