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

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

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

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

- \infty

Solution steps

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

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

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

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

= \frac{- \infty}{\frac{π}{2}}

Apply Infinity Property:

\frac{- \infty}{c} = - \infty

= - \infty

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

x \to 0 lim (\frac{3}{sin ( x )})

x \to 1 lim (\frac{1}{ln ( x )} - \frac{1}{x})

x \to - 2 - lim (\frac{x ^{2}}{3 x + 6})

t \to 1 lim (t^{2})

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