What is the limit as x approaches 0 of 1/x sinh(x) ?

The limit as x approaches 0 of 1/x sinh(x) is 1

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limit as x approaches 0 of 1/x sinh(x)

x \to 0 lim (\frac{1}{x} sinh (x))

1

Solution steps

x \to 0 lim (\frac{1}{x} sinh (x))

Simplify

\frac{1}{x} sinh (x) : \frac{sinh ( x )}{x}

= x \to 0 lim (\frac{sinh ( x )}{x})

Apply L'Hopital's Rule

= x \to 0 lim (\frac{cosh ( x )}{1})

Plug in the value

x = 0

= \frac{cosh ( 0 )}{1}

Simplify

\frac{cosh ( 0 )}{1} : 1

= 1

What is the limit as x approaches 0 of 1/x sinh(x) ?
The limit as x approaches 0 of 1/x sinh(x) is 1