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

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

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

a \to 0 lim (cot (a) - csc (a))

0

Solution steps

a \to 0 lim (cot (a) - csc (a))

Multiply by the conjugate of

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

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

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

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

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

a \to 0 lim (1) = 1

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

= - \frac{1}{\infty}

Apply Infinity Property:

\frac{c}{\infty} = 0

= 0

x \to - 1 lim (\frac{3 x ^{2}}{2 x - 1})

x \to 0 + lim (x^{2 x + 1})

x \to 2 + lim (\frac{∣ x - 2 ∣}{2 - x})

x \to 1 lim (- x^{2} + 3 x)

x \to - 3 lim (\frac{x ^{6} - 729}{x + 3})

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