What is the limit as x approaches 0 of ((e^x-e^{-x}-2x))/(1-sin(x)) ?

The limit as x approaches 0 of ((e^x-e^{-x}-2x))/(1-sin(x)) is 0

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limit as x approaches 0 of ((e^x-e^{-x}-2x))/(1-sin(x))

x \to 0 lim (\frac{( e ^{x} - e ^{- x} - 2 x )}{1 - sin ( x )})

0

Solution steps

x \to 0 lim (\frac{e ^{x} - e ^{- x} - 2 x}{1 - sin ( x )})

Plug in the value

x = 0

= \frac{e ^{0} - e ^{- 0} - 2 \cdot 0}{1 - sin ( 0 )}

Simplify

\frac{e ^{0} - e ^{- 0} - 2 \cdot 0}{1 - sin ( 0 )} : 0

= 0

What is the limit as x approaches 0 of ((e^x-e^{-x}-2x))/(1-sin(x)) ?
The limit as x approaches 0 of ((e^x-e^{-x}-2x))/(1-sin(x)) is 0