What is the limit as x approaches 0+of sinh(x)cot(x) ?

The limit as x approaches 0+of sinh(x)cot(x) is 1

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limit as x approaches 0+of sinh(x)cot(x)

x \to 0 + lim (sinh (x) cot (x))

1

Solution steps

x \to 0 + lim (sinh (x) cot (x))

Rewrite for L'Hopital

= x \to 0 + lim (\frac{sinh ( x )}{\frac{1}{c o t ( x )}})

Apply L'Hopital's Rule

: x \to 0 + lim (\frac{cosh ( x )}{sec ^{2} ( x )})

= x \to 0 + lim (\frac{cosh ( x )}{sec ^{2} ( x )})

Plug in the value

x = 0

= \frac{cosh ( 0 )}{sec ^{2} ( 0 )}

Simplify

\frac{cosh ( 0 )}{sec ^{2} ( 0 )} : 1

= 1

x^{2}, at x = 2

\frac{\partial}{\partial x} (\frac{4 - x ^{2} y}{2 x})

\frac{\partial}{\partial x} (3 x y^{2} + 20 x^{2} y^{3})

y^{^{''}} + 2 y^{^{'}} + 2 y = 0, y (\frac{π}{4}) = 2, y^{^{'}} (\frac{π}{4}) = - 2

\int \frac{3 x ^{2} + 17 x + 32}{x ^{3} + 8 x ^{2} + 16 x} d x

What is the limit as x approaches 0+of sinh(x)cot(x) ?
The limit as x approaches 0+of sinh(x)cot(x) is 1