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wimma
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Homework Statement
lim (x-> infinity) sinh(x)sinh(e^(-x))
Homework Equations
None really.
The Attempt at a Solution
L'Hospital?
The limit of sinh(x) as x approaches infinity is also infinity. This is because the hyperbolic sine function grows exponentially as x increases.
The limit of sinh(e^(-x)) as x approaches infinity is 0. This is because as x approaches infinity, e^(-x) approaches 0 and sinh(0) = 0.
The product of two limits is equal to the limit of the product. In this case, the limit of sinh(x) as x approaches infinity multiplied by the limit of sinh(e^(-x)) as x approaches infinity is equal to infinity multiplied by 0, which is equal to 0.
The limit of sinh(x)sinh(e^(-x)) as x approaches infinity is equal to 0, while the limit of sinh(x) as x approaches infinity is equal to infinity. This means that the limit of the product is significantly smaller than the limit of sinh(x) alone.
This limit tells us that as x approaches infinity, the function sinh(x)sinh(e^(-x)) approaches 0. This means that the value of the function gets closer and closer to 0 as x gets larger, but never actually reaches 0. This behavior is known as asymptotic behavior.