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

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

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

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

1

Solution steps

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

Apply L'Hopital's Rule

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

= 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

\frac{6 x ^{2} + 2 x + 4}{x}

y^{^{''}} + 3 y^{^{'}} - 2 y = 0

\frac{d y}{d x} = 4 e^{x - y}

(x y + y^{2} + y) d x + (x + 2 y) d y = 0

y^{^{'}} = cos (x + y)

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