Question

Show that the function sinx + cosx iS everywhere continuous
Please solve it

Answer 1

This can be proven in a number of ways. Firstly as Olivier Begassat noted that it is a composition of continues functions and thus is continues itself.

Another way you can see it is by observing that:

limx↓πf(x)=|sin(π)+cos(π)|=limx↑πf(x)=limx→πf(x)=1

limx↓πf(x)=|sin⁡(π)+cos⁡(π)|=limx↑πf(x)=limx→πf(x)=1

So the function exists and is well defined in the limit. Therefore it is conitnues