Question

Limit Question, Retyping using equation editor

Answer 1

\[\lim_{x \rightarrow \inf}\frac{ \sqrt{5+4x^2} }{ 4+3x }\]

So far I have done the following.
\[\lim_{x \rightarrow \inf}\frac{ \sqrt{5+4x^2} }{ 4+3x} \times \frac{ \sqrt{5+4x^2} }{ \sqrt{5+4x^2} } = \frac{ 5+4x^2 }{(4+3x)\sqrt{5+4x^2} }\]

Answer 2

not sure what to go from here

Answer 3

HI!!

Answer 4

do it with your eyeballs, ignore all but the highest powers

Answer 5

If i do it with my eyes I get inf/inf

Answer 6

you get
\[\frac{\sqrt{4x^2}}{3x}=\frac{2x}{3x}=\frac{2}{3}\] that is all

Answer 7

humm, is that the same if you was to go to -inf ?

Answer 8

no

Answer 9

How do i think about it if I was to approach -inf

Answer 10

if you go to \(-\infty\) the numerator is positive but the denominator is negative so you get \(-\frac{2}{3}\)

Answer 11

Alright thanks, I am going to review some lectures. This topic is kind of confusing!

Answer 12

\[\color\magenta\heartsuit\]