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=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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