Recent content by Gaz031

\int (|1 + x| - |1 - x|) dx x>1: \int (|1 + x| - |1 - x|) dx = \int (1+x)-(x-1) dx = \int 2 dx = 2x + A -1<x<1: \int (|1+x| - |1-x|) dx = \int (1+x)-(1-x) dx = \int 2x dx = x^{2} + B x<-1: \int(|1+x| - |1-x|) dx = \int (-1-x)-(1-x) dx = \int -2 dx = -2x+C

Is that right to say? You're assuming the derivative of \sin x is \cos x to prove \lim_{x \rightarrow 0} \frac{\sin x}{x} = 1 but actually the limit (together with the AoL) is normally used to prove the derivative of \sin x. Normally one would use the sandwich rule to find the limit.

Besides your expression for the derivative don't forget to state x > 0 , x \neq 1 as a derivative at x_{1} needs to be defined over some interval x_{1}-R<x<x_{1}+R

You could start by doing: \cos ((arc cos p + arc cos q) + arc cos r)=-1 \cos (arc cosp + arc cosq)cos(arc cosr) - \sin (arc cosp+arc cosq) \sin (arc cosr)=-1 rpq-r\sin (arc cosp) \sin (arc cosq))-q\sin (arc cosp) \sin (arc cosr) - p\sin (arc cos q)\sin (arc cosr) = -1 You can then use...

Not in the UK. 5-16=Primary school > Secondary school. (compulsary). 16-18=Sixth form/college (A-Levels) (Voluntary). 18- =University (Voluntary).

if y=f(x): \frac{dy}{dx}=\lim_{h \rightarrow 0} \left(\frac{f(x+h)-f(x)}{h}\right)

This isn't exactly homework but I thought it was too basic to justify putting this post in the general math section. My question is: why is arcoshx defined as: arcoshx=ln[x+rt(x^2-1)] and not +-ln[x+rt(x^2-1)] ? Is it simply to keep it as a one to one function? I know that to have an inverse a...

Thanks for the replies people. I heard that but am prepared to work on it, provided it doesn't require divine inspiration! I've heard analysis tends to be one of the hardest first year courses. That looks quite good. I was looking at also as a methods reference but the one you suggested...

You can either use the CAST quadrant diagram or the cos(A+B) formulae, but both rely on you knowing cos(pi/6)=(rt3)/2

What distinguishes stochastic calculus from other varieties? Is it the type applied in statistics? I haven't really done much statistics at A-Level (I chose 'pure' and mechanics) so perhaps I should look into it. I do prefer things like problem solving to computation though(the piece of stats I...

Hi there, I'm currently finishing my A-Level exams (UK system) and provided I achieve my offer will be going to university in autumn to studying single honours mathematics (4 Yr MMath/Msci). I'm going to have a 3 month gap between my last exam and starting university, so I obviously want to...

Just use the SUVAT equations. Consider vertically: u = 35sin40, S = 0, a = -9.8, t = ? You'll get a quadratic by using the correct formulae. One solution is t=0 (at the start). The other is when the projectile touches the ground again (the time of flight).

Briefly: If you have the displacement as a function of time you can differentiate to get the velocity. You can differentiate the velocity to get acceleration. Similarly, you can integrate the acceleration to the velocity to the displacement. However, you need to add your constants carefully...

I know the length of AB is root3. The line AB has equation 3y+3x-9=0. Neither do i understand how you can have a three dimensional angle without making a whole lot of extra degrees or using two angles and reinventing trigonometry.

I can't draw 3d shapes but I've sketched it as best as i can. Where did you get the coordinates 1,1,0 and -.5,-.5,3 from? What mathematical process? I hate crappy 3d vectors especially with this crappy book that throws you a question without any method for doing it.