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

The limit as x approaches pi/2 of sec^2(x) is infinity

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limit as x approaches pi/2 of sec^2(x)

x \to \frac{π}{2} lim (sec^{2} (x))

\infty

Solution steps

x \to \frac{π}{2} lim (sec^{2} (x))

x \to a lim [f (x)]^{b} = [x \to a lim f (x)]^{b}

With the exception of indeterminate form

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

Apply the common limit:

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

= (- \infty)^{2}

Apply Infinity Property:

(- \infty)^{n} = \infty, n

is even

= \infty

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