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Popular >

arctanh(0)

Solution

arctanh (0)

Solution

0

Solution steps

arctanh (0)

Use the Hyperbolic identity:

arctanh (x) = \frac{ln ( \frac{1 + x}{1 - x} )}{2}

= \frac{ln ( \frac{1 + 0}{1 - 0} )}{2}

\frac{ln ( \frac{1 + 0}{1 - 0} )}{2} = 0

\frac{ln ( \frac{1 + 0}{1 - 0} )}{2}

\frac{1 + 0}{1 - 0} = 1

\frac{1 + 0}{1 - 0}

Add the numbers:

1 + 0 = 1

= \frac{1}{1 - 0}

Subtract the numbers:

1 - 0 = 1

= \frac{1}{1}

Apply rule

\frac{a}{1} = a

= 1

= \frac{ln ( 1 )}{2}

Simplify

ln (1) : 0

ln (1)

Apply log rule:

lo g_{a} (1) = 0

= 0

= \frac{0}{2}

Apply rule

\frac{0}{a} = 0, a \neq = 0

= 0

= 0

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Frequently Asked Questions (FAQ)

What is the value of arctanh(0) ?
The value of arctanh(0) is 0