Is 1/(1+e^-(x)) equivalent to 1-e^-(x) when x is very large?

In summary, the conversation involved discussing an exam question where the asker used an approximation to prove a theorem regarding hole density in semiconductors. They noticed the limiting behavior of the approximation as x goes from 50 to infinity and questioned why their answer was marked incorrect. The expert suggests asking the person who marked it incorrect for further clarification.
  • #1
Cilly28
1
0
Long story short, I said on an exam that...

1/(1+e^-(x)) =~(is nearly equal to) 1-e^-(x); note* x > 50 , they are also inversely proportional when x<-50 but that isn't specific to the problem

I used this to prove a theorem regarding hole density in semiconductors ""when x is very very large""...It was marked incorrectly but the question stated that the magnitude of x would be >50. I noticed the limiting behavior of this as it goes from 50 to infinity and they appear to be equal, especially when approximations are made in the 'books proof' to simplify the equation, mainly throwing low integers away that do not effect a number of much higher magnitude.

If I made a correct approximation and still obtained the same result equation, just because I did it differently shouldn't make it incorrect, would anyone agree?
 
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  • #2
The apporximation is correct. I suggest you ask the person who marked it incorrect explain why. It may be that you were supposed to justify the approximation in more detail.
 

FAQ: Is 1/(1+e^-(x)) equivalent to 1-e^-(x) when x is very large?

What are exponential equivalents?

Exponential equivalents are mathematical expressions that represent the same value, but are written in different forms. They are typically used to simplify complex equations or to compare values.

How do I convert exponential equivalents?

To convert exponential equivalents, you can use the rules of exponents. For example, to convert from scientific notation to standard form, you move the decimal point the same number of places as the exponent. For converting between different exponential forms, you can use logarithms.

Why are exponential equivalents important?

Exponential equivalents are important because they allow us to express numbers in a more simplified or standardized form. They also help us to solve complex equations and make comparisons between different values more easily.

What are some examples of exponential equivalents?

Some examples of exponential equivalents include scientific notation (1.23 x 10^4), standard form (12,300), and exponential form (2^5). Other examples may include equations involving logarithms, such as log base 10 and ln (natural logarithm).

How can I use exponential equivalents in real life?

Exponential equivalents can be used in many real life situations, such as in science and engineering, finance, and statistics. For example, scientists may use exponential equivalents to express extremely large or small numbers, while financial analysts may use them to compare different investment options. In everyday life, exponential equivalents can also be helpful in understanding and interpreting data or making informed decisions.

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