Hyperbolics Flashcards
(15 cards)
What is the equation for hyperbolic cosine?
y = cosh x
What is the definition of cosh x?
cosh x = (e^x + e^(-x)) / 2
What is the limit of cosh x as x approaches 0?
as x → 0, cosh x → 1
What is the limit of cosh x as x approaches negative infinity?
as x → -∞, cosh x → ∞
What is the definition of sinh x?
sinh x = (e^x - e^(-x)) / 2
What is the limit of sinh x as x approaches 0?
sinh x → 0 as x → 0
What is the limit of sinh x as x approaches negative infinity?
sinh x → -∞ as x → -∞
What is the domain of cosh x?
The domain of cosh x is all real numbers (zeR).
What is the range of cosh x?
The range of cosh x is y ≥ 1.
What is the domain of sinh x?
The domain of sinh x is all real numbers (zeR).
What is the range of sinh x?
The range of sinh x is all real numbers (zeR).
What is the domain of tanh x?
The domain of tanh x is all real numbers (zeR).
What is the range of tanh x?
The range of tanh x is -1 < tanh z < 1.
What is the hyperbolic function identity for cosh 2x?
cosh 2x = cosh² x + sinh² x
What is the derivative of arsinhx
1/(1+x²)^0.5
