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

The limit as x approaches 0+of csc(x)-cot(x) is 0

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limit as x approaches 0+of csc(x)-cot(x)

x \to 0 + lim (csc (x) - cot (x))

0

Solution steps

x \to 0 + lim (csc (x) - cot (x))

Multiply by the conjugate of

csc (x) - cot (x) : \frac{1}{csc ( x ) + cot ( x )}

= x \to 0 + lim (\frac{1}{csc ( x ) + cot ( 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

= \frac{lim _{x \to 0 +} ( 1 )}{lim _{x \to 0 +} ( csc ( x ) + cot ( x ) )}

x \to 0 + lim (1) = 1

x \to 0 + lim (csc (x) + cot (x)) = \infty

= \frac{1}{\infty}

Apply Infinity Property:

\frac{c}{\infty} = 0

= 0

n = 5 \sum \infty \frac{6}{n ^{2} - 1}

5^{x}

(- 4, - 4), (- 3, 0)

\frac{\partial}{\partial x} (18 x^{2} y + 12 x y^{2})

arcsin (\frac{x ^{2} - 1}{x})

What is the limit as x approaches 0+of csc(x)-cot(x) ?
The limit as x approaches 0+of csc(x)-cot(x) is 0