Find limit in comments

Question

anonymous · Answer

$$\lim_{x \rightarrow \infty}\frac{ 5x }{ x+3 }$$

anonymous · Answer

howsit hatnn

hartnn · Answer

divide numerator and denominator by x

anonymous · Answer

hmmm thats what was confusing me. I just need a course on infinite limits in general my study guide didnt go through it at all.

anonymous · Answer

$$\frac{ 5 }{ 1+\frac{ 3 }{ x } }$$

hartnn · Answer

here, generally we try to bring the terms in the from of 1/x or 1/x^2 or 1/x^n
so that we can put them as 0
because, when x-> $\infty$, 1/x^n ->0
yes, so now put 1/x = 0 there.

anonymous · Answer

so i just have 5

hartnn · Answer

yup

anonymous · Answer

and its like this with every type of lim to infinity?

hartnn · Answer

almost every...there maybe some special case where you need to do something else.
in all types of limits with terms x^n

anonymous · Answer

could you provide an example of this special case?

hartnn · Answer

like trignometric limits, 
i can think of this easy one:
lim x->$\infty$    x sin(1/x)
here u put 1/x=y

anonymous · Answer

as y? now there are two variables??

hartnn · Answer

no, when x-> infinity , y-> 0 
so the limit gets converted to 
lim y->0  sin y/y 
which is 1