- #1
bobsmith76
- 336
- 0
Homework Statement
why is the answer not e^10x ?
If you ignore the e's it should be
5x - 5x + 5x - - 5x, or
5x - 5x + 5x + 5x, which is 10x
Why Isn't the Answer to the Hyperbolic Function e^10x?
- Thread starter bobsmith76
- Start date
Click For Summary
Homework Help Overview
The discussion revolves around a misunderstanding related to hyperbolic functions and their properties, specifically questioning why a certain expression does not simplify to e^10x.
Discussion Character
- Conceptual clarification, Assumption checking
Approaches and Questions Raised
- Participants explore the implications of ignoring the exponential terms and question the nature of the functions involved. There is a focus on the properties of exponentiation and hyperbolic functions.
Discussion Status
Some participants have offered hints regarding the properties of exponentials, while others express confusion about the underlying algebraic principles. Multiple interpretations of the problem are being explored without a clear consensus.
Contextual Notes
There is an indication that the original poster may be conflating linear and hyperbolic functions, and assumptions about the manipulation of exponential terms are being questioned.
why is the answer not e^10x ?
If you ignore the e's it should be
5x - 5x + 5x - - 5x, or
5x - 5x + 5x + 5x, which is 10x
- #2
Dickfore
- 2,987
- 5
If you ignored the e's, it wouldn't be a hyperbolic function, but a linear function.
- #3
bobsmith76
- 336
- 0
well, i still don't see any reason why the answer is not e^10x
- #4
Dickfore
- 2,987
- 5
Hint:
[tex] e^{x} + e^{y} \neq e^{x + y}[/tex]
For example: Take [itex]x = y = 0[/itex] and compare the two sides of this unequality.
[tex] e^{x} + e^{y} \neq e^{x + y}[/tex]
For example: Take [itex]x = y = 0[/itex] and compare the two sides of this unequality.
- #5
Curious3141
Homework Helper
- 2,864
- 89
Bob, this is basically [itex]\frac{a+b}{2} + \frac{a-b}{2} = \frac{a}{2} + \frac{b}{2} + \frac{a}{2} - \frac{b}{2} = (2)(\frac{a}{2}) = a[/itex]. Simple algebra. Here [itex]a = e^{5x}[/itex] and [itex]b = e^{-5x}[/itex].
But your comment indicates a deeper confusion about exponents and algebraic principles. I would suggest that it might be a good idea to review basic algebra including the rules of exponentiation.
But your comment indicates a deeper confusion about exponents and algebraic principles. I would suggest that it might be a good idea to review basic algebra including the rules of exponentiation.
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