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

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

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

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

1

Solution steps

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

Apply L'Hopital's Rule

: x \to 0 lim (\frac{sech ^{2} ( x )}{1})

= x \to 0 lim (\frac{sech ^{2} ( x )}{1})

Plug in the value

x = 0

= \frac{sech ^{2} ( 0 )}{1}

Simplify

\frac{sech ^{2} ( 0 )}{1} : 1

= 1

\frac{d}{d x} (\frac{1}{3} tan (x))

y = x - x

0.5 e^{- 4.5 t} sin (2 π t)

\frac{d y}{d x} = 3 x - y + 4

\int \frac{( ln ( x ) ) ^{50}}{x} d x

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