Limits question

Question

lim as x approaches inifnity (square root of x+3 minus square root of n)

Can I say that its infinity - infinity hence its a 0?

Answer 1

sqr(x+3) - sqr(x) = f(x)

x f(x)

-2 1-1.4i =an imaginary number

0 sqr3 = 1.7

.5 1.87-.7 = 1.17

1 2-1.7= .3

2 2.2-1.4 =.8

3 2.45-1.73 = .72

6 3-2.45 = .55

97 10-9.85= .15

997 31.62-31.58= .04

It does look as if as x goes to infinity, f(x) approaches zero

but infinity minus infinity doesn't necessarily = 0. infinity minus infinity is an indeterminate form.

x+3 - x has a limit of 3 as x approaches infinity

but if you placed x with infinity, infinite+3 = infinity and infinity minus infinity is not zero or 3, it's indeterminate.

(3x^2)/x^2 = 3 yet if you placed x by infinity, 3 times infinity^2 = infinity squared, it would be infinity^2/infinity^2 = 1

Cantor developed the mathematics of infinity, which drove him crazy. Literally. He ended up in an insane aslyum from thinking about infinity. You get paradoxes that don't seem to make sense, but they are.

sqr(x+3) - sqrx is the graphically the same as the top half of one parabola minus the top of another parabola. top halves of x =y^2 and x=y^2 +3, the curves approach each other as x approaches infinity