What is the limit as x approaches pi/2+of 1/x sec(x) ?

The limit as x approaches pi/2+of 1/x sec(x) is -infinity

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limit as x approaches pi/2+of 1/x sec(x)

x \to \frac{π}{2} + lim (\frac{1}{x} sec (x))

- \infty

Solution steps

x \to \frac{π}{2} + lim (\frac{1}{x} sec (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 (\frac{1}{x}) \cdot x \to \frac{π}{2} + lim (sec (x))

x \to \frac{π}{2} + lim (\frac{1}{x}) = \frac{2}{π}

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

= \frac{2}{π} (- \infty)

Apply Infinity Property:

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

= - \infty

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What is the limit as x approaches pi/2+of 1/x sec(x) ?
The limit as x approaches pi/2+of 1/x sec(x) is -infinity