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

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

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

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

0

Solution steps

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

Multiply by the conjugate of

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

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

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

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

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

h \to 0 lim (1) = 1

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

= - \frac{1}{\infty}

Apply Infinity Property:

\frac{c}{\infty} = 0

= 0

x \to 0 lim (x^{(x^{x})})

x \to \infty lim (\frac{- 7 x ^{2} - 1}{x ^{2} + x 4 + 7 x ^{2} + 1})

x \to - 1 lim (\frac{x}{x ^{3} + 4 x})

x \to 0 lim (x ln (6 x))

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

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