1 / 0 = ± ∞,
And also 1 / ∞ = 0,
If we divide anything with small number we get a large number in comparison of those when we divide anything with large number. So if we divide 1 with 0+ (it indicates small positive Numbers) we get + ∞ number and if we divide 1 with 0- (indicate small negative numbers) we get negative infinity -∞. If we want to add two numeric values such as 7 and 4 then the result will be,
7 + 4 = 11,
If we want to add any value ‘x’ (such that ‘x’ is not negative infinity) with positive infinity then in that case the result is always +∞.
So+∞ + x = + ∞ if ‘x’ not equals to -∞.
If we want to subtract any value from negative infinity where the value of ‘x’ should not be zero then in that case the result is always -∞. It is shown below,
-∞- x = -∞ if and only if x not equals to -∞.
There are some other Properties of Division with infinity. If we want to divide ‘∞’ from any value of ‘x’ where ‘x’ is greater than 0 and ‘x’ not equals to ‘∞’ then∞ / x = ∞ where x > 0 and ‘x’ not equals to ‘∞’.
Like -∞/ x = -∞ where x> 0 and ‘x’ not equals to -∞.
∞ / x = -∞ where x< 0 and ‘x’ is not equals to -∞.
Limits at infinity are used to show or indicate the nature of the function when independent variable increases or decreases.
x→+∞lim f(x) = K,
or x→-∞lim f(x) = K.