What is the limit as x approaches pi/2-of xsec(x) ?

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

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limit as x approaches pi/2-of xsec(x)

x \to \frac{π}{2} - lim (x sec (x))

\infty

Solution steps

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

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

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

= \frac{π}{2} \cdot \infty

Apply Infinity Property:

c \cdot \infty = \infty

= \infty

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