Help needed for concept of limit question!!?

Question

Please help me with this question..i'm clueless about it

limit 3 +2x/4x - 1
x → ∞

Answer given is 1/2...how is that possible?

Answer 1

Ah... divide 3 + 2x by x... then divide 4x - 1 by x...

Now you have 3/x + 2 on the top of the fraction or dividing line...

On the bottom of the fraction or dividing line you have 4 - 1/x..

Anything divided by something going toward infinity goes toward 0....( 1 divided by 100 is one hundredth... 1 divided by 1000 is one thousandth... & so on)

So you end up w/ 0 + 2 divided by 4 - 0...

Which is 2 divided by 4...

This is quite formulaic... it is something that students tend to learn off & then act as if it is 'obvious'... as nonstandard analysis shows it is by no means 'obvious' that the way we do calculus is the right way...

& for future reference, it really does make things easier on yourself & others if you use brackets...

limit (3 + 2x) / (4x - 1), where lim gets nfinitely large..

Answer 2

it is the limit as x--> ∞ of (3 + 2x)/(4x + 1), right? The answer to that question actually is 1/2. The way you look at it is that when x approaches ∞, the +3 on top and +1 on bottom are going to become negligible (adding a 3 doesn't make a difference when we're talking about ∞). Thus, it's really the limit as x --> ∞ of 2x/4x. Now you can cancel out the x's, and you get 2/4. Thus, the limit as x-->∞ is 2/4, or 1/2.

Answer 3

When solving limit questions where x approaches infinity we look at the most dominant terms:

In this qn the 2x/4x is the most dominant. The 3 and the -1 will become insignificant as x approaches infinity

hence
limit 3 +2x/4x - 1
x → ∞

= limit 2x/4x
x → ∞

= limit 2/4
x → ∞

= 2/4 = 1/2

Answer 4

To find the limit as x approaches infinity you must divide each term by the x value raise to the highest power in the denomanator. so...

limx>infinity = 3 +2x/4x - 1
limx>infinity = (3/x +2x/x)/(4x/x - 1/x)

As x approaches infinity -1/x and 3/x approach 0 and so you get

limx>infinity = (0 +2)/(4 - 0)
limx>infinity = (2)/(4) = 1/2

Answer 5

limit (3 +2x)/(4x - 1)
x → ∞
= limit (3/x +2)/(4 - 1/x)
x → ∞
=2/4
=1/2

Answer 6

Is the expression (3+2x)/(4x-1) ?

If it is, you can see by inspection that the constants (3 in the numerator and -1 in the denominator) won't contribute much to the answer as x gets really huge.

Answer 7

take x common in the numerator and denominator

(3/x + 2)/ (4 - 1/x)
taking limit (1/x) term be zero
= 2/4
= 1/2

Answer 8

The series a million/n does certainly converge to 0 as n procedures infinity. it particularly is the series of __partial sums__ of this series which diverges. i.e. the series of sums a million a million+ a million/2 a million +a million/2 + a million/3 a million + a million/2 + a million/3 + a million/4 ... ... ... keeps on transforming into for ever with none decrease. on the same time as the guy words of this series do strategies-set 0, their sum will at last exceed any quantity you care to call. wish this helps make sparkling issues.

Answer 9

divide the nr and dr by x
lim x> inf (3/x)+2/4-(1/x)
as x tends to infinity 1/x will tend to zero
so the limit=2/4=1/2

Answer 10

Go to this website for answer.
http://www.mathnerds.com/mathnerds/links/links.aspx