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So... 2-1/1+(1)(2) = \tan (\tan^{-1}(2)-\tan^{-1}(1)) = 1/3 therefore: \tan^{-1}(2)-\tan^{-1}(1) = \tan^{-1}(\frac{1}{3})? Is that the only way, i.e. there is no super fast formula i.e. using some relationship between the two numbers, 1 and 2etc?

Hi guys, quick question: How is \tan^{-1}(2)-\tan^{-1}(1) = \tan^{-1}(\frac{1}{3}) ??? I don't understand how it works, is there a particular rule??? How would I show/prove the result it in an exam? Basically, I had the expression: \textrm{t}=\frac{4\tan^{-1}(2)-\pi }{4\textrm{kc}}...

How do I simplify tan^{-1}(a)\, -\, \tan^{-1}(b)? In my question there is an expression: And v is for velocity, u, and k are constants. And I need to get v in terms of t. And probably the best idea would be to simplify Thanks for the help guys.

Hi guy's just something I'm curious about involving velocity, specifically in the situation where there is simple harmonic motion. So we know the expression that v^2 = (n^2)(a^2 - x^2) --> where a refers to amplitude (maximum displacement). And thus v = +/- (n)[(a^2 - x^2)^0.5] ------- (1)...

Thankyou, I also got 400, just a question, I'm familiar with terms acceleration, velocity and displacement. But what is this +ve, -ve (acceleration, velocity, displacement) business? I don't know what it is? Could someone please explain? Thank you.

Let's say v = 40 - 10 t so v = 0, when t=4 (i.e. particle is stationary at t=4) What is the acceleration at t=4 (i.e. what is the acceleration when v=0 (particle is stationary))? Is it just -10m/s/s?? or is it like some undefined crap? Thanks, appreciate the help! :) EDIT: Also, say the...

i DOn't get it? Isn't it just 8P4 = 1680 ways?

Re: Volumes -- parabolic cross sections --- problem with finding area of cross-sectio Thanks mate, took me a while to understand what the hell the working out meant, but I got there in the end :) So just to make sure -- that is the best/fastest/only way to find the equation of the parabola...

Re: Volumes -- parabolic cross sections --- problem with finding area of cross-sectio simpson's rule you say? so how would i apply it to this question? and how would i obtain the function values? i mean i don't even know what the function is lol (i.e. equation of parabola)...

Hi guys, I'm having a problem with a question from Cambridge: EX 6.3 Q7 Q. The base of a particular solid is x^2 + y^2 = 4. Find the volume of the solid if every cross-section perpendicular to the x-axis is a parabolic segment with axis of symmetry passing through the x-axis and height the...

shit, I meant root(9-x^2)

Hi guys just wondering, is there any quicker way of integrating 9-x^2 without using the substitution x=3sinA?? Because part of a volumes question in my 4U trials involved integrating 9-x^2 --> And i used the substitution of x=3sinA, which resulted in a further 8 lines of working out. However...

Q. The angle between the line y=x/A and the tangent to the curve y=Ax^2 at x=1 is 45 degrees Find the value(s) of A ---------------------- Here's what I did gradient of y=x/A is 1/A Also y=Ax^2 --> dy/dx = 2Ax --> at x=1, gradient = 2A so tan(45) = |(2A - 1/A)/(1+2) =|(2A^2 - 1)/(3A)|...

ahhhhhhhhhh ok thank you very very much I get it know :)

Hi guys, here's the question: Q. Consider the function f(x) = 0.5(arcsinx) Find the area of the region bounded the curve, the x-axis and the line x=1 ---------------------------- My solution (which is wrong) http://imageshack.us/photo/my-images/810/inverse.jpg/# (Zoom the browser in with...

ahh ok thanks.... perhaps the question is wrong

Hi guys, quick question here: Q. Solve for x and y arcsinx + arccosy = pi/12 --- (1) arcsiny - arccosx = 7pi/12 ---- (2) --------- My working (someone please point out what is wrong with it) (1) + (2) arcsinx - arccosx + (arcsiny + arccosy) = 2pi/3 arcsinx - arccosx = 2pi/3 - pi/2 = pi/6...

^^repped

Ahh thank you now I know what the question was asking for. But there's another question I'm having trouble with: Q. The region inside the circle x^2 + y^2 = a^2 is rotated about the line x=2a to form a solid called a torus. Find it's volume by the means of cylindrical shells. ----------- My...

umm... sorry i don't get it, what does it mean by "rotating the arc"? isn't an arc just a 1 dimensional line? What exactly are you meant to do? Thanks