Question

Find limit in comments

Answer 1

\[\lim_{x \rightarrow \infty}\frac{ 5x }{ x+3 }\]

Answer 2

howsit hatnn

Answer 3

divide numerator and denominator by x

Answer 4

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.

Answer 5

\[\frac{ 5 }{ 1+\frac{ 3 }{ x } }\]

Answer 6

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.

Answer 7

so i just have 5

Answer 8

yup

Answer 9

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

Answer 10

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

Answer 11

could you provide an example of this special case?

Answer 12

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

Answer 13

as y? now there are two variables??

Answer 14

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