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

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

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limit as θ approaches 0 of cot(θ)-csc(θ)

θ \to 0 lim (cot (θ) - csc (θ))

0

Solution steps

θ \to 0 lim (cot (θ) - csc (θ))

Multiply by the conjugate of

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

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

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

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

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 _{θ \to 0} ( 1 )}{lim _{θ \to 0} ( cot ( θ ) + csc ( θ ) )}

θ \to 0 lim (1) = 1

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

= - \frac{1}{\infty}

Apply Infinity Property:

\frac{c}{\infty} = 0

= 0

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

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

x \to 1 lim (x^{\frac{1}{2 x - 2}})

x \to 0 + lim (\frac{1}{x ^{4}})

x \to \infty lim (2 x^{2} - 4 x - 2)

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