- #1

- 415

- 0

why the solution develops [tex]e^{-x}[/tex] and puts 0.5

and not [tex]e^{+x}[/tex] and putting -0.5

?

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In summary, the conversation discusses the calculation of e^{-0.5} and the confusion about why the solution involves e^{-x} and -0.5 instead of e^{+x} and 0.5. The expert clarifies that both methods should give the same answer and explains the Taylor's series for e^{-x} and e^x to demonstrate that they are equivalent.

- #1

- 415

- 0

why the solution develops [tex]e^{-x}[/tex] and puts 0.5

and not [tex]e^{+x}[/tex] and putting -0.5

?

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- #2

Science Advisor

Homework Helper

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I suspect that both them method your book gives and your method would give the same answer. Have you tried it?

- #3

- 415

- 0

but in the first we have libnits series and on the other not

so its not the same

why they are not the same?

- #4

Science Advisor

Homework Helper

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[tex]\sum_{n=0}^\infty \frac{(-1)^n}{n!}x^n[/itex].

In particular,

[tex]e^{-0.5}= \sum_{n=0}^\infty \frac{(-1)^n}{n!}(0.5)^n[/itex]

The usual Taylor's series for [itex]e^x[/itex] is, of course,

[tex]\sum_{n=0}^\infty \frac{1}{n!}x^n[/itex]

and now

[tex]e^{-0.5)= \sum_{n=0}^\infty \frac{1}{n!}(-0.5)^n= \sum_{n=0}^\infty \frac{1}{n!}(-1)^n(0.5)^n[/tex]

[tex]= \sum_{n=0}^\infty \frac{(-1)^n}{n!}(0.5)^n[/tex]

They are exactly the same.

An exponent error is a mathematical mistake that occurs when calculating numbers with exponents. It can happen when the exponent is entered incorrectly or when the order of operations is not followed correctly.

To avoid making exponent errors, it is important to double check your work and follow the correct order of operations. You can also use a calculator or write out the steps of your calculation to ensure accuracy.

The correct order of operations when dealing with exponents is PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). This means that exponents should be calculated before any multiplication, division, addition, or subtraction.

Yes, an exponent error can definitely change the final answer. Even a small mistake in the exponent can result in a significantly different answer.

If you realize you made an exponent error after finishing your calculation, you should go back and correct the mistake. If you are unable to do so, it is best to redo the entire calculation to ensure the correct answer.

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