What is the limit as x approaches 0 of x^2csc(x) ?

The limit as x approaches 0 of x^2csc(x) is 0

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limit as x approaches 0 of x^2csc(x)

x \to 0 lim (x^{2} csc (x))

0

Solution steps

x \to 0 lim (x^{2} csc (x))

Rewrite for L'Hopital

= x \to 0 lim (\frac{x ^{2}}{\frac{1}{c s c ( x )}})

Apply L'Hopital's Rule

= x \to 0 lim (\frac{2 x}{cos ( x )})

Plug in the value

x = 0

= \frac{2 \cdot 0}{cos ( 0 )}

Simplify

\frac{2 \cdot 0}{cos ( 0 )} : 0

= 0

What is the limit as x approaches 0 of x^2csc(x) ?
The limit as x approaches 0 of x^2csc(x) is 0