What is the limit as x approaches 0 of (x*sh(2x))/(ch(4x)-1) ?

The limit as x approaches 0 of (x*sh(2x))/(ch(4x)-1) is 0

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limit as x approaches 0 of (x*sh(2x))/(ch(4x)-1)

x \to 0 lim (\frac{x \cdot s h ( 2 x )}{c h ( 4 x ) - 1})

0

Solution steps

x \to 0 lim (\frac{x s h ( 2 x )}{c h ( 4 x ) - 1})

Plug in the value

x = 0

, assuming the function is continuous at this point

= \frac{0 \cdot s h ( 2 \cdot 0 )}{c h ( 4 \cdot 0 ) - 1}

Simplify

= 0

x \to \infty lim (\frac{0}{5})

x \to \infty lim ((cos (x))^{\frac{1}{( x ^{2} )}})

x \to 1 lim (\frac{x ^{11} + 2 x - 3}{x ^{7} + x ^{2} - x - 1})

x \to 0 lim (\frac{1}{x} - \frac{1}{e ^{2} - 1})

x \to - 3 lim (\frac{x + 1}{x ^{2} - 9})

What is the limit as x approaches 0 of (x*sh(2x))/(ch(4x)-1) ?
The limit as x approaches 0 of (x*sh(2x))/(ch(4x)-1) is 0