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

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

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

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

0

Solution steps

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

Multiply by the conjugate of

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

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

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

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

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

y \to 0 lim (1) = 1

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

= - \frac{1}{\infty}

Apply Infinity Property:

\frac{c}{\infty} = 0

= 0

x \to 2 lim (2^{x})

x \to 0 lim (\frac{2 sin ( 4 x )}{x})

x \to 0 + lim ((x) (ln (x)))

x \to 0 + lim (ln (e^{x} - 1))

x \to + 0 lim (\frac{( cos ( m x ) - cos ( n x ) )}{x ^{2}})

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