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What is the Value of e-∞?
By BYJU'S Exam Prep
Updated on: September 25th, 2023
The number ‘e’ is known as Euler’s number which is an irrational number. It is a numerical constant having a value of 2.718281828459045..so on, or you can say e∞ is equal to ( 2.71…)∞. But when it is negative then the value of e-∞ is Zero. Learn why the value of e-∞ is 0.
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Answer:
The value of e-∞ is Zero and the value of e∞ is ( 2.71…)∞
Let us learn the explanation
Suppose X =e^(-infinity)
We can write it as X=1/e^infinity
When we multiply e infinite times with e, it will become very large that it will reach infinity
So, X=1/infinity
As infinity is a very large number and dividing 1 by a very large number gives a number very close to zero but not exactly zero.
So, X is a very small positive number as it reaches zero from positive side.
So, simply it is not zero because when e is increasing at a very high rate and it is tending towards a very large number and when e is raised to the -∞ then it becomes a very small number and hence tends to zero.
Summary:
What is the Value of e-∞?
E, also known as Euler’s number, is an irrational number. The value of e∞ is ( 2.71…)∞, whereas, on the other hand, the value of e-∞ is Zero.
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