- #1
SteveBell
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Homework Statement
Lim (E^x-1)^(1/x)
x->Infinito
L'Hospital?
Homework Equations
Lim (1+1/x)^x=E
x->Infinito
The Attempt at a Solution
Help!
The limit of (E^x+1)^1/x as x approaches infinity is equal to e, the base of the natural logarithm. This can be mathematically proven using L'Hopital's rule or by recognizing that the expression approaches e^1, which is equal to e.
No, the limit of (E^x+1)^1/x is not equal to zero. As x approaches infinity, the expression approaches e, which is a non-zero value. This can also be seen by plugging in larger and larger values for x, which will result in a larger and larger value for the expression.
Yes, the limit of (E^x+1)^1/x can be evaluated without using L'Hopital's rule. As x approaches infinity, the expression approaches e, which can be determined by recognizing the pattern and properties of exponential functions.
As x approaches negative infinity, the limit of (E^x+1)^1/x does not exist. This is because the expression will approach e for positive values of x, but will approach 0 for negative values of x. Therefore, the limit is undefined at negative infinity.
Yes, the limit of (E^x+1)^1/x can be evaluated for non-integer values of x. As long as x is a real number, the limit will still approach e as x approaches infinity. This can be seen by plugging in decimal values for x and observing that the expression approaches e.