Showing piece-wise function continuous

[ChiralSuperfields]

Homework Statement

Please see below

Relevant Equations

Please see below

For this,

,
The solution is,

However, should they not write $f(x) = \cos x$ on $[\frac{pi}{4}, \infty)$

Many thanks!

 

[FactChecker]

Do you mean right after the "Similarly,"? It wouldn't hurt, but I think that it is easy enough to follow the logic without saying that. Initially, you should be in the habit of stating everything. After a while, that becomes tedious and both you and the reader will be happy if you skip obvious things. You must be careful though, what you skip.

 

[ChiralSuperfields]

Do you mean right after the "Similarly,"? It wouldn't hurt, but I think that it is easy enough to follow the logic without saying that. Initially, you should be in the habit of stating everything. After a while, that becomes tedious and both you and the reader will be happy if you skip obvious things. You must be careful though, what you skip.

Thank you for you reply @FactChecker!

No sorry I meant right after the "Since f(x) = Sinx on ..."

Many thanks!

 

[FactChecker]

Thank you for you reply @FactChecker!

No sorry I meant right after the "Since f(x) = Sinx on ..."

Many thanks!

Oh. The reason for not including the point $\pi/4$ is that the rest of the sentence is only about continuity on $(-\infty, \pi/4)\cup(\pi/4, \infty)$. So there was no need to include $\pi/4$. It wouldn't have hurt to include it.