What is the limit as x approaches 0 of (sinh(2x))/x ?

The limit as x approaches 0 of (sinh(2x))/x is 2

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limit as x approaches 0 of (sinh(2x))/x

x \to 0 lim (\frac{sinh ( 2 x )}{x})

2

Solution steps

x \to 0 lim (\frac{sinh ( 2 x )}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{cosh ( 2 x ) \cdot 2}{1})

= x \to 0 lim (\frac{cosh ( 2 x ) \cdot 2}{1})

Plug in the value

x = 0

= \frac{cosh ( 2 \cdot 0 ) \cdot 2}{1}

Simplify

\frac{cosh ( 2 \cdot 0 ) \cdot 2}{1} : 2

= 2

x \to a lim (\frac{x ^{5} - a ^{5}}{x ^{4} - a ^{4}})

x \to \infty lim (\frac{3 x - cos ( x )}{2 x + sin ( x )})

x \to \infty lim (\frac{4 x ^{2} + 5 x - 1}{x ^{2} - 7 x + 29})

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

x \to 0 lim (\frac{tan ( x )}{x} cos (x))

What is the limit as x approaches 0 of (sinh(2x))/x ?
The limit as x approaches 0 of (sinh(2x))/x is 2