What is the limit as x approaches 6+of sec((pix)/4) ?

The limit as x approaches 6+of sec((pix)/4) is infinity

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limit as x approaches 6+of sec((pix)/4)

x \to 6 + lim (sec (\frac{π x}{4}))

\infty

Solution steps

x \to 6 + lim (sec (\frac{π x}{4}))

Express with sin, cos

= x \to 6 + lim (\frac{1}{cos ( \frac{π x}{4} )})

For

x

approaching

6

from the right

, x > 6 \Rightarrow cos (\frac{π x}{4}) > 0

The denominator is a positive quantity approaching 0 from the right

= \infty

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What is the limit as x approaches 6+of sec((pix)/4) ?
The limit as x approaches 6+of sec((pix)/4) is infinity