Limit tan(sqrt(x)) answer check please

[synergix]

limit tan(sqrt(x)) answer check please!:)

Homework Statement

tan(sqrt(x))
locate discontinuities

The Attempt at a Solution

tan(sqrt(x))=
sin(sqrt(x))/cos(sqrt(x))

so x cannot= (pi/2)² + (pi)n when n is an integer

I am just wondering if this is correct

 

[Mark44]

Homework Statement

tan(sqrt(x))
locate discontinuities

The Attempt at a Solution

tan(sqrt(x))=
sin(sqrt(x))/cos(sqrt(x))

so x cannot= (pi/2)² + (pi)n when n is an integer

I am just wondering if this is correct

No.
There are a couple of things to consider:

1. the domain of sqrt(x)
2. the domain of the tangent function.

Changing tan(x) to sin(x)/cos(x) isn't any help, I don't believe.

If we let y = sqrt(x), y will be in the domain of the tangent function provided that y = $\pi/2 + k\pi$
IOW, $\sqrt{x} = \pi/2 + k\pi$, where k is an integer.
I believe you were on this track, but solved this equation incorrectly. Try again.

 

[synergix]

what does IOW mean? x must be greater then one and cannot equal ((pi/2 + (pi)n)^2 when n is a positive integer right?

 

[Dick]

IOW means either 'In Other Words' or 'Isle of Wight'. Pick one. I just looked it up. Mark44 is saying tan(sqrt(x)) isn't defined if sqrt(x)=pi/2+k*pi where k is an integer. Solve for x. It's not quite what you said it was.

 

[synergix]

If I were to say tan(sqrt(x)) is not defined if x is less then zero or equal to (Pi/2+K*pi)^2 where k is an integer would that be correct?

 

[Dick]

If I were to say tan(sqrt(x)) is not defined if x is less then zero or equal to (Pi/2+K*pi)^2 where k is an integer would that be correct?

Yes.