Question

which function has an asymptote at x=pi/2?


a) y= sec x


b) y= cot x


c) y= csc x


d) y= cos x

Answer 1

Answer:

Step-by-step explanation:

Note that y= sec x is the same as y = 1 / cos x, and that cos x is 0 at π/2.  Division by zero is not defined.  Thus, x cannot = π/2, and there is a vertical asymptote there.

Thus, the first answer choice, y = sec x, is the correct one.

Answer 2

The function at which there is an asymptote at x=(π/2) is y=sec (x).

What is an asymptote?

A straight line that is constantly approaching a curve but does not meet at an infinite distance is known as an asymptote.

Which one is an asymptote?

As we can see in the given option y= sec x can be written as,

$y = sec\ x = \dfrac{1}{cos\ x}$

And at x =(π/2), cos x = 0 = cos 90°,

therefore,

$y = sec\ x = \dfrac{1}{cos\ x} = \dfrac{1}{0}$

As the value  $\dfrac{1}{0}$ is undefined, there is an asymptote at (π/2) exist.

Hence, the function at which there is an asymptote at x=(π/2) is y=sec (x).

Learn more about Asymptote:

https://brainly.com/question/8493280