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 )})

Plug in the value

x = 0

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

Simplify

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

= 1

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