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

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

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

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

0

Solution steps

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

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

With the exception of indeterminate form

= \frac{lim _{x \to \infty} ( tanh ( x ) )}{lim _{x \to \infty} ( x )}

x \to \infty lim (tanh (x)) = 1

x \to \infty lim (x) = \infty

= \frac{1}{\infty}

Apply Infinity Property:

\frac{c}{\infty} = 0

= 0

x \to \infty + lim (2)

x \to 0 lim (\frac{x}{x ^{3} + 5 x})

x \to 1 - lim (- \frac{1}{x ^{2} + 6 x - 7})

x \to 0 lim (ln (\frac{x ^{2}}{2}))

x \to 1 lim (6 x + 1)

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