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

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

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limit as x approaches 0 of 4/(xcsc(x))

x \to 0 lim (\frac{4}{x csc ( x )})

4

Solution steps

x \to 0 lim (\frac{4}{x csc ( x )})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

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

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

With the exception of indeterminate form

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

x \to 0 lim (1) = 1

x \to 0 lim (x csc (x)) = 1

= 4 \cdot \frac{1}{1}

Simplify

= 4

y = 3 (x^{3} - x), y = 0

\int_{- 1}^{2} (2 x - 1) (4 x + 5) d x

y^{^{'}} = - \frac{x}{y} + \frac{( x ^{2} + y ^{2} )}{y}

\int_{c}^{d} \int_{a}^{b} 1 + x + y d x d y

\int \frac{1}{2 x ^{2} + 4} d x

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