x approaches to infinity means

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x approaches to infinity means

Meaning of the phrase” x approaches to infinity” 

Suppose a variable x assumes in succession a series of value as multiple of 10 start from 1

x approaches to infinity means

x approaches to infinity means

X=1, 10, 100, 1000, 10000,……………………..

This result in power form

x=1, 10, 10², 10 ³, …………………………10 power n…………….

It is clear that x is becoming Larger and Larger than power n increase, and we can be made as Large As we please by taking n sufficiently large. This unending increase of x is symbology written as” x → ∞”(x converges to undefined) or” x approaches to infinity”or” x tends to infinity”

Meaning of the phrase” x approaches to zero” 

Suppose a variable x assumes in succession a series of value as fraction 1 / 2 of power natural number, e.g (1,2,3,4…………..n…..) start from 1

NOTE:

The symbol   x  →  0   is quite different from x = 0

(i)   x  →  0 means that x is very close to zero but not actually zero

(ii) x = 0 mean that x is actually zero

X = 1, 1/2, 1/4, 1/8, 1/16,………………..

This can be written in the form

1,1/2,1/2², 1/2³,1/2⁴, ………1/2ⁿ,……..

We notice that x is becoming smaller and smaller than n increase and can be made as small as we place by n sufficiently by large. This unending decrease of x is symbolically written as x → 0 and is read as “x approaches to zero”or” x tends to zero.

Meaning of the phrase” x approaches to a”

Symbolically, it is written as “x →  a” which means that x is sufficiently close to but different from the number a that is x → a become smaller and smaller as we please but x  → a ≠ 0

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