4U Maths Question Thread

[Maz]

Actually it said to integrate then differentiate. So the fundamental theorem of calculus allows us to work our way around that.

how would you do that? 

[RuiAce]

how would you do that? 

The old fashioned and very VERY tedious way of doing that is the one I posted at the very start with the logs and stuff.

The more recent post is a much faster way to get things done.

[Maz]

ohhh...
thankyou so so soooo much 

[amandali]

not sure why its D

[jamonwindeyer]

not sure why its D

Hey amandali!

Okay, this question requires a little bit of thought, but it is actually not too difficult!

Consider the equation for the roots (just using normal alphabetical characters instead of Greek):



If all of these roots were real, then this equation wouldn't make sense, since the square root of a real is always positive. Thus, we must have a complex root in there somewhere. However, by the complex conjugate root theorem, one complex root for a polynomial automatically means that the conjugate is also a root. Thus, since we require one complex root for the equation to make sense, we must have at least two complex roots by this theorem. Hence, the answer is D.

I hope this helps! 

[amandali]

how to solve this?
please help thanks

[katherine123]

im not sure how to determine whether point P lies above or below the x axis
for questions like   arg(z-1) = arg(z+1) + pie/4

[jakesilove]

how to solve this?
please help thanks

Hey!

Below is my solution. Generally, this is the method you'll need to use for any similar question so I would recommend memorising it!



Jake

[jakesilove]

im not sure how to determine whether point P lies above or below the x axis
for questions like   arg(z-1) = arg(z+1) + pie/4

Hey!

Presumably, you are being asked to sketch something like the graph



So first, you solve and draw the general curve (I believe that this is a circle?). Then, I would choose an easy point (generally, 0+0i) and see whether it falls within or without the given question.

We can see that



Which is clearly greater than Pi/4! Therefore, whichever section the value 0+0i is in, should be filled in!

I hope I've understood your question correctly.

Jake

[Neutron]

Hello friends!

I was wondering whether you could help me integrate tan^2 (x) sec^2 (x) dx ? Thank you, I seem to be having trouble ughhh

Neutron

[jakesilove]

Hello friends!

I was wondering whether you could help me integrate tan^2 (x) sec^2 (x) dx ? Thank you, I seem to be having trouble ughhh

Neutron

Hey Neutron!

This question looks deceptively difficult, but the answer ends up being quite straight forward! The trick is recognising what you need to use (ie. reverse chain rule), and not falling into the trap of using a more complicated method (ie. Integration by parts). Anyway, my answer is below, hope it helps!



Jake

[RuiAce]

Alternatively, if the reverse chain rule is a bit too hard to see, just apply the substitution u=tan(x).

At the Ext 2 level though, you do want to practice identifying the reverse chain rule

[jamonwindeyer]

Alternatively, if the reverse chain rule is a bit too hard to see, just apply the substitution u=tan(x).

At the Ext 2 level though, you do want to practice identifying the reverse chain rule

Just to see that alternative method, it would go something like below! (I would probably not have spotted the reverse chain rule, I rely on substitution way too much  ):

[Neutron]

Hey Neutron!

This question looks deceptively difficult, but the answer ends up being quite straight forward! The trick is recognising what you need to use (ie. reverse chain rule), and not falling into the trap of using a more complicated method (ie. Integration by parts). Anyway, my answer is below, hope it helps!

(Image removed from quote.)

Jake

Omg I'm honestly feeling so dumb right now, thank you so much guys :') I kept trying to expand the sec^2 and the tan^2 and ugh that was a mess oops

[jamonwindeyer]

Omg I'm honestly feeling so dumb right now, thank you so much guys :') I kept trying to expand the sec^2 and the tan^2 and ugh that was a mess oops

Don't feel dumb Neutron, not being given the substitution makes it hard to see! Interesting approach, you mean pythagorean identities and such? Must have been nasty 

I once got told, Differentiation is a Science, and Integration is an Art. Differentiation has set procedures and rules we follow to get our answers. Integration is a little more intuitive, and in my opinion, much more difficult. Practice makes perfect I think 

Be sure to keep hitting us up with questions!!