What is the limit as x approaches 0 of (e^x+e^{-x})/(e^x-e^{-x)} ?

The limit as x approaches 0 of (e^x+e^{-x})/(e^x-e^{-x)} is diverges

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limit as x approaches 0 of (e^x+e^{-x})/(e^x-e^{-x)}

x \to 0 lim (\frac{e ^{x} + e ^{- x}}{e ^{x} - e ^{- x}})

diverges

Solution steps

x \to 0 lim (\frac{e ^{x} + e ^{- x}}{e ^{x} - e ^{- x}})

x \to a - lim f (x) \neq = x \to a + lim f (x)

then the limit does not exist

x \to 0 + lim (\frac{e ^{x} + e ^{- x}}{e ^{x} - e ^{- x}}) = \infty

x \to 0 - lim (\frac{e ^{x} + e ^{- x}}{e ^{x} - e ^{- x}}) = - \infty

= diverges

\frac{d}{d x} (1 - x)

(0, - 4), (1, 2)

x y^{^{'}} + 3 y = 3 e^{x}

(1 - 5 y + x) \frac{d y}{d x} + y = 5 x - 1

y^{'} (t) = 10 - e^{y}, y (0) = 1

What is the limit as x approaches 0 of (e^x+e^{-x})/(e^x-e^{-x)} ?
The limit as x approaches 0 of (e^x+e^{-x})/(e^x-e^{-x)} is diverges