Limits of Infinity: Does f(x) Exist?

[phymatter]

Is it so that for lim_x->infinity f(x) to exist ,
lim_x->+infinity f(x) and lim_x->-infinity should exist and be equal ? if so then why ?

 

[LCKurtz]

Is it so that for lim_x->infinity f(x) to exist ,
lim_x->+infinity f(x) and lim_x->-infinity should exist and be equal ? if so then why ?

No, it isn't so. Look at f(x) = Arctan(x).

 

[phymatter]

No, it isn't so. Look at f(x) = Arctan(x).

Are you sure , because i.a. maron single variable calculus says that lim_x->infinity (2x²+3)^1/2/(4x+2) does not exist for the same reason .

 

[Office_Shredder]

$$\lim_{x\to \infty}$$ IS the limit as x goes to positive infinity.

 

[Mark44]

Are you sure , because i.a. maron single variable calculus says that lim_x->infinity (2x²+3)^1/2/(4x+2) does not exist for the same reason .

$$\lim_{x \to \infty}\frac{\sqrt{2x^2 + 3}}{4x + 2} = \frac{1}{4}$$

Is I.A. Maron the author of a calculus text? I never heard of it.

 

[HallsofIvy]

You have to be careful with your conventions. Normally, with the real numbers, "$\infty$" means "$+\infty$. However, with the "one-point compactification" of the real numbers (not commonly used for Calculus problems!) we have just the one "point at infinity".