What is the limit as x approaches infinity of 1/6 ln(tanh((3x)/2)) ?

The limit as x approaches infinity of 1/6 ln(tanh((3x)/2)) is 0

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limit as x approaches infinity of 1/6 ln(tanh((3x)/2))

x \to \infty lim (\frac{1}{6} ln (tanh (\frac{3 x}{2})))

0

Solution steps

x \to \infty lim (\frac{1}{6} ln (tanh (\frac{3 x}{2})))

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= \frac{1}{6} \cdot x \to \infty lim (ln (tanh (\frac{3 x}{2})))

Apply the Limit Chain Rule:

0

= \frac{1}{6} \cdot 0

Simplify

= 0

x \to 0 + lim ((e^{x} - 1) ln (x))

x \to 2 lim (3 x + 3)

x \to 0 + lim (4 x^{l n (x)})

x \to 1 lim (\frac{2 x - 2}{3 26 + x - 3})

x \to 3 lim (\frac{12 - x}{x + 3})

What is the limit as x approaches infinity of 1/6 ln(tanh((3x)/2)) ?
The limit as x approaches infinity of 1/6 ln(tanh((3x)/2)) is 0