What is the degree of e^(y/x)?
- TomVLv 76 months ago
The concept of degree of an expression is only applicable to polynomials.
The expression e^(y/x) is not a polynomial.
The expression has no degree.
The question is analogous to asking the color of anger.
- Demiurge42Lv 76 months ago
Only polynomials have a degree. e^(y/x) isn't a polynomial.
- KrishnamurthyLv 76 months ago
The degree of e^(y/x) is (y/x).
- DixonLv 76 months ago
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- JOHNLv 76 months ago
The degree of y/x is deg (y) - deg (x) = 1 - 1 = 0.
e^(y/x) is a function of y/x and has degree 0.
An illustration from physics might help clarify this.
Dimensionally, whenever the exponential appears
in a physical equation, the argument of the
exponential must be a dimensionless pure number,
or else the expression doesn't make sense and can't
be a term of a true equation. For instance Planck's
radiation law states E(ν) = hν/[e^(hν/kT) - 1]. Now
[hν] = [joules] and [ kT] = [joules] (k = Boltzmann's
constant, T = Kelvin temperperature). so we have
joules/joules = pure number and e^(hν/kT) makes
sense. Further, on te left of the radiation law we
have joules and on the right we have joules/pure
number = joules. Thus the hν/kT of e^(hν/kT) has
to be a pure number for all to make sense.
- Steve ALv 76 months ago
It would be y/x degree
- 6 months ago
probably a tan...