Sales Toll Free No: 1-800-481-2338

# Calculus Infinity

TopIn Calculus infinity is a symbol which is represented by ∞. It basically denotes a large number. As we all know that if we divide any number from zero the result is always zero but if in case if we divide zero in any numeric term then the result is infinity which approach in both directions positive and negative. We can show that,
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.