What is the limit as x approaches pi/2+of x/(cot(x)) ?

The limit as x approaches pi/2+of x/(cot(x)) is -infinity

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limit as x approaches pi/2+of x/(cot(x))

x \to \frac{π}{2} + lim (\frac{x}{cot ( x )})

- \infty

Solution steps

x \to \frac{π}{2} + lim (\frac{x}{cot ( x )})

Use the basic trigonometric identity:

\frac{1}{cot ( x )} = tan (x)

= x \to \frac{π}{2} + lim (x tan (x))

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

With the exception of indeterminate form

= x \to \frac{π}{2} + lim (x) \cdot x \to \frac{π}{2} + lim (tan (x))

x \to \frac{π}{2} + lim (x) = \frac{π}{2}

x \to \frac{π}{2} + lim (tan (x)) = - \infty

= \frac{π}{2} (- \infty)

Apply Infinity Property:

c \cdot (- \infty) = - \infty

= - \infty

r \to 0 lim (\frac{sin ( r )}{r})

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

t \to - \infty lim (t^{3} e^{t})

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

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

What is the limit as x approaches pi/2+of x/(cot(x)) ?
The limit as x approaches pi/2+of x/(cot(x)) is -infinity