What is the limit as x approaches 0 of x(csc(x)) ?

The limit as x approaches 0 of x(csc(x)) is 1

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limit as x approaches 0 of x(csc(x))

x \to 0 lim (x (csc (x)))

1

Solution steps

x \to 0 lim (x csc (x))

Rewrite for L'Hopital

= x \to 0 lim (\frac{x}{\frac{1}{c s c ( x )}})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{1}{cos ( x )})

= x \to 0 lim (\frac{1}{cos ( x )})

Plug in the value

x = 0

= \frac{1}{cos ( 0 )}

Simplify

\frac{1}{cos ( 0 )} : 1

= 1

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y^{^{''}} - \frac{2}{7} y^{^{'}} + \frac{1}{49} y = 0

x^{2} \frac{d y}{d x} + 2 x y = 1

x^{3} - 6 x^{2} - 34 x + 40, at x = - 2

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What is the limit as x approaches 0 of x(csc(x)) ?
The limit as x approaches 0 of x(csc(x)) is 1