What is the limit as x approaches 0 of xcsc(4x) ?

The limit as x approaches 0 of xcsc(4x) is 1/4

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limit as x approaches 0 of xcsc(4x)

x \to 0 lim (x csc (4 x))

\frac{1}{4}

Decimal Notation

0.25

Solution steps

x \to 0 lim (x csc (4 x))

Express with sin, cos

= x \to 0 lim (\frac{x}{sin ( 4 x )})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{1}{cos ( 4 x ) \cdot 4})

= x \to 0 lim (\frac{1}{cos ( 4 x ) \cdot 4})

Plug in the value

x = 0

= \frac{1}{cos ( 4 \cdot 0 ) \cdot 4}

cos (4 \cdot 0) \cdot 4 = 4

= \frac{1}{4}

11

\frac{d}{d x} (\frac{2 x}{4 x - 1})

y, (9 x e^{- \frac{1}{y ^{3}}} - 20 x^{3})

\frac{d}{d x} ((3 - 2 x)^{5})

\frac{d y}{d x} = \frac{y}{( x + y )}

What is the limit as x approaches 0 of xcsc(4x) ?
The limit as x approaches 0 of xcsc(4x) is 1/4