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

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

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

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

0

Solution steps

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

Multiply by the conjugate of

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

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

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

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

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

t \to 0 lim (1) = 1

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

= - \frac{1}{\infty}

Apply Infinity Property:

\frac{c}{\infty} = 0

= 0

x \to 5 lim (x - 1)

x \to \infty lim (x^{2} + 7)

z \to \infty lim (\frac{4 z ^{5}}{z ^{5} - 42 z})

x \to 3 lim (\frac{x - 3}{x})

x \to - 3 lim (\frac{x ^{2} - 9}{3 + 3})

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