Yeah, you shouldn't force your religious beliefs onto others and extremist acts in the name of religion should definitely be condemned. That being said, I don't think it's fair to point out what extremist Muslims do and then generalise this to the entire group because most Muslims are good...
Personally, I think the problem isn't that they exist - any competent adult is free to do whatever they like if it doesn't harm others. What Trump would do though is prevent these ideologies that people may regard as "weird" from being shoved down your throat and help stop things that a minority...
expanding on this, would just say that such a method just isn't rigourous but if there are applicable qs in the hsc u would use it cos they don't rlly care abt this stuff.
I was arguing that the answers u obtain using these methods aren't the same function because of the inherent restriction u put on certain values, which can cause problems such as what u pointed out in evaluating definite integrals. I am also fully aware of the trick, in fact I've used it before...
What I mean is just because the original integrand is undefined doesn't mean the primitive is also undefined at that point. This is because the primitive could have a vertical tangent at the point where the original function is undefined (e.g. 1/sqrt(1-x^2) is undefined at x = +-1 yet it's...
this is irrelevant since the original function being undefined at a point doesn't mean it's primitive is also undefined, eg f(x) = 1/(sqrt(1-x^2)). In this case the manipulation works (I think) and the results end up being the same due to how we define trig functions most likely, but as a...